[tex]A_2[/tex] = 18°
[tex]A_3[/tex] = 4(18°) = 72°
Step-by-step explanation:Given:
One angle in the triangle is 90°One angle that isn't 90° is 4 times larger than another angle that isn't 90°Angles:
[tex]A_1[/tex] = 90°
[tex]A_2[/tex] = x
[tex]A_3[/tex] = 4x
Solution Pathway:
Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:
sum of the interior angles = 180°90° + x + 4x = 180°Now let's solve for x.
90 +x + 4x = 18090 + 5x = 1805x = 90x = 18°Now that we know x is 18°, lets plug this value into the two unknown acute angles.
[tex]A_2[/tex] = 18°[tex]A_3[/tex] = 4(18°) = 72°Answer:
72 degrees and 18 degrees.
Step-by-step explanation:
If the 2 angles are x and y, we have the system:
x + y = 90 (as it is a right triangle)
x = 4y (given).
Substitute x =- 4y in the first equation:
4y + y = 90
5y = 90
y = 18.
So x + 18 = 90
x = 90 - 18
x = 72.
Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4 <= x <= 5 and 6<= y<= 16. How many different triangles with these properties could be constructed?
(A) 110
(B) 1,100
(C) 9,900
(D) 10,000
(E) 12,100
Answer:
(C) 9900
Step-by-step explanation:
The right triangle which right angle is at P and PR is parallel to the x-axis can have 4 sets (A,B,C,D as illustrated) of format depends on which direction is the right angle located.
each set have
(1+2+3+4+5+6+7+8+9) x (1+2+3+4+5+6+7+8+9+10) = 45 x 55 = 2475 right triangles
4 sets: 2475 x 4 = 9900
A girl is now one-fourth as old as her father, and in seven years, she will be one-half as old as her father was twelve years ago. What are her and her father's present ages?A. father's age = 20; daughter's age = 5B. father's age = 52; daughter's age = 13C. father's age = 76; daughter's age = 19
Answer:
Option B - father's age = 52; daughter's age = 13
Step-by-step explanation:
Given : A girl is now one-fourth as old as her father, and in seven years, she will be one-half as old as her father was twelve years ago.
To find : What are her and her father's present ages?
Solution :
Let the father's present age is 'x'.
A girl is now one-fourth as old as her father.
i.e. Girl age is [tex]\frac{x}{4}[/tex]
In seven years, she will be one-half as old as her father was twelve years ago.
i.e. [tex]\frac{x}{4}+7=\frac{1}{2}(x-12)[/tex]
[tex]\frac{x}{4}+7=\frac{x}{2}-6[/tex]
[tex]\frac{x}{4}-\frac{x}{2}=-6-7[/tex]
[tex]\frac{x-2x}{4}=-13[/tex]
[tex]-x=-52[/tex]
[tex]x=52[/tex]
The father's age is 52 years.
The daughter's age is [tex]\frac{52}{4}=13[/tex]
Therefore, option B is correct.
Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
4.59
0.07
6.55
5.60
(I have more questions in my recently asked too that I could really use help with as soon as possible.) Thank you.
Answer:
4.59
Step-by-step explanation:
sin(angle) = opposite / hypotenus
Use the information to answer the questions.
In triangle ABC, a = 11 in., measure angle B=70 deg and
c = 9 in.
Which information about the triangle is given?
Answer:
Part 1) The length of two sides and the measure of the included angle (Side-Angle-Side)
Part 2) [tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]
Part 3) [tex]b=11.6\ in[/tex]
Step-by-step explanation:
we have
In the triangle ABC
[tex]a=11\ in\\c=9\ in\\B=70^o[/tex]
Part 1) Which information about the triangle is given?
In this problem we have the length of two sides and the measure of the included angle (Side-Angle-Side)
see the attached figure to better understand the problem
Part 2) Which formula can you use ti find b?
I can use the law of cosines
[tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]
we have
[tex]a=11\ in\\c=9\ in\\B=70^o[/tex]
substitute the given values
[tex]b^2=11^2+9^2-2(11)(9)cos(70^o)[/tex]
[tex]b^2=202-67.72[/tex]
[tex]b=11.59\ in[/tex]
Part 3) What is b, rounded to the nearest tenth?
Remember that
To Round a number
a) Decide which is the last digit to keep
b) Leave it the same if the next digit is less than [tex]5[/tex] (this is called rounding down)
c) But increase it by [tex]1[/tex] if the next digit is [tex]5[/tex] or more (this is called rounding up)
In this problem we have
[tex]11.59\ in[/tex]
We want to keep the digit [tex]5[/tex]
The next digit is [tex]9[/tex] which is 5 or more, so increase the "5" by 1 to "6"
therefore
[tex]b=11.6\ in[/tex]
Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.
However small the difference between two population proportion ,for sufficiently large sample size, the null hypothesis of equalpopulation proportions is likely to be rejected.
The statement is true; as sample size increases, even small differences between two population proportions can lead to the rejection of the null hypothesis. The decreasing standard error with larger samples increases the test statistic, leading to smaller p-values. However, practical significance should also be considered alongside statistical significance.
Explanation:The statement regarding the hypothesis test for two population proportions is true. As the sample size increases, even a very small difference between the two population proportions becomes significant. This is because with larger sample sizes, the standard error of the difference between the two proportions decreases, which increases the test statistic used in hypothesis testing. As a result, we are more likely to reject the null hypothesis of equal population proportions if the sample size is sufficiently large, assuming there is indeed a small actual difference.
The null hypothesis typically states that there is no effect or no difference, and in the case of two population proportions, it states that the proportions are equal. When we conduct a hypothesis test, we calculate the probability of observing our sample data, or something more extreme, given that the null hypothesis is true. This probability is known as the p-value. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.
However, it's important to note that the ability to detect small differences with large samples does not imply that those differences are practically significant, only statistically so. Therefore, in addition to hypothesis testing, it's essential to consider effect size and practical significance when interpreting results.
Percent and Percent Change - Item 884404Question 4 of 6 Martina makes $8 as a regular employee. If she becomes a manager, she will increase her hourly rate by 30%. Use the drop-down menus to build an equation that could be used to find a manager's hourly pay rate, x
Answer:
10.4
Step-by-step explanation:
8+8*0.3
= 10.4
Hope that helps
Answer:
10.4
Step-by-step explanation:
8+8*0.3
= 10.4
Hope that helps
In a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. What is the ratio of nickels to dimes?
Answer:
6:5
Step-by-step explanation:
It is given that a pot worth $2.35 and there are 6 quarters, 5 dimes, 5 pennies, the rest of the coins are nickels.
We know that
$1 = 100 cents
1 penny = 1 cent = $0.01
1 nickel = 5 cents. = $0.05
1 dime = 10 cents. = $0.10
1 quarter = 25 cents = $0.25
The value of 6 quarters is
[tex]6\times 0.25=1.50[/tex]
The value of 5 dimes is
[tex]5\times 0.10=0.50[/tex]
The value of 5 pennies is
[tex]5\times 0.01=0.05[/tex]
Let x be the number of nickels. So, the value of x nickels is
[tex]x\times 0.05=0.05x[/tex]
Total value of 6 quarters, 5 dimes, 5 pennies, and x nickels is
[tex]Total =1.50+0.50+0.05+0.05x[/tex]
[tex]Total =2.05+0.05x[/tex]
It is given that the pot worth is $2.35.
[tex]2.05+0.05x=2.35[/tex]
Subtract 2.05 from both sides.
[tex]0.05x=0.30[/tex]
Divide both sides by 0.05.
[tex]x=6[/tex]
The number of nickels is 5.
[tex]\dfrac{Nickel}{Dimes}=\dfrac{6}{5}=6:5[/tex]
Therefore, the ratio of nickels to dimes is 6:5.
In a pot worth $2.35 containing 6 quarters, 5 dimes, 5 pennies, and some nickels, the ratio of nickels to dimes is 6:5.
To find the ratio of nickels to dimes, we need to determine the number of nickels and dimes in the pot. We know that there are 6 quarters, 5 dimes, and 5 pennies in the pot, which is a total of 16 coins. Therefore, the number of nickels should be the difference between the total number of coins and the sum of quarters, dimes, and pennies.
The total value of the coins in the pot is $2.35. Since 6 quarters are worth $1.50, 5 dimes are worth $0.50, and 5 pennies are worth $0.05, the remaining value should come from the nickels.
Thus, the value of the nickels is $2.35 - $1.50 - $0.50 - $0.05 = $0.30. Since each nickel is worth $0.05, the number of nickels is $0.30 ÷ $0.05 = 6.
The ratio of nickels to dimes is therefore 6:5, which means that for every 6 nickels, there are 5 dimes.
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What is the Common difference in the sequence 10,20,30,40,50...?
Answer:
10
Step-by-step explanation:
divide the last number by the previous number
Answer:
10
Step-by-step explanation:
If you calculate it correctly, every number in front of that number it 10 above.
Evaluate the expression \dfrac{x^5}{x^2} x 2 x 5 start fraction, x, start superscript, 5, end superscript, divided by, x, squared, end fraction for x=2x=2x, equals, 2.
Answer:
8
Step-by-step explanation:
Fill in the variable value and do the arithmetic.
[tex]\dfrac{2^5}{2^2}=\dfrac{32}{4}=8[/tex]
___
Of course, the fraction can be simplified first:
[tex]\dfrac{x^5}{x^2}=x^{5-2}=x^3\\\\2^3=8[/tex]
To evaluate the expression, substitute x with 2, simplify the exponents, and perform the multiplication
Explanation:To evaluate the expression \dfrac{x^5}{x^2} \times 2 \times 5
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Write the equation of the line that has a slope of 2 and passes through the point (-3,4).
A) y = 2x - 2
B) y = 2x + 2
C) y = 2x + 7
D) y = 2x + 10
Answer:
The answer to your question is letter D
Step-by-step explanation:
Data
slope = m = 2
Point (-3, 4)
Process
1.- Substitute the data in the line equation
y - y1 = m(x - x1)
y - 4 = 2 (x + 3)
2.- Expand
y - 4 = 2x + 6
3.- Solve for y and simplify
y = 2x + 6 + 4
y = 2x + 10
Answer:
y=2x+10
Step-by-step explanation:
Andre rents a bike for a day. The rental changes can be determined by the equation: R = $0.5d, where R is rental changes and d is number of days she rents the bike. Calculate the unit rate.
Answer:the unit rate is $0.5
Step-by-step explanation:
Andre rents a bike for a day. The rental changes can be determined by the equation: R = $0.5d, where R is rental changes and d is number of days she rents the bike.
The unit rate multiplied by the number of days for which the bike was rented would give the total rental charge. From the given equation, the unit rate would be $0.5
The length of the top of a computer desk is 2 1/4 feet longer than it's width. If it's width measures y feet, express its length as an algebraic expression in y
Answer:
Step-by-step explanation:
The top of the computer desk is rectangular in shape.
Let y represent the width of the rectangle.
The length of the top of the computer desk is 2 1/4 feet longer than its width. Converting 2 1/4 feet to improper fraction, it becomes 9/4 feet. Therefore, the algebraic expression of the length of the of the top of the computer desk in terms of y would be
Length = y + 9/4
You begin with $90 in your savings account and your friend begins with $35 in her savings account. You deposite $10 in savings each week, and your friend deposites $15 in savings each week
Answer:
Part a) The graph in the attached figure (see the explanation)
Part b) The friend is not correct
Step-by-step explanation:
The questions are
a. Write and graph a system of linear equations that represent the amounts in each of your savings accounts
b. Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer.
Part a)
Let
x ----> the number of weeks
y ---> the amount in the saving account
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
In this problem we have
Your saving accounts
The slope is equal to [tex]m=\$10\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$90[/tex]
substitute
[tex]y=10x+90[/tex] ----> equation A
Your friend saving accounts
The slope is equal to [tex]m=\$15\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$35[/tex]
substitute
[tex]y=15x+35[/tex] ----> equation B
using a graphing tool
the graph in the attached figure
Part b) Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer
we know that
When solving a system of equations by graphing, the solution of the system is the intersection point both graphs
In this problem, the intersection point is (11,200)
That means ----> In 11 weeks, both you and your friend have the same amount of money saved up, $200
Therefore
The friend is not correct
The width of a rectangle is 4 more than half the length.
If the perimeter of the rectangle is 74, what is the width?
Perimeter of rectangle: P = 2l + 2w
Width= ? Length= ?
Answer:
The answer to your question is L = 22; w = 15
Step-by-step explanation:
Data
length = L
width = w
Perimeter = 74
Condition
w = L/2 + 4
Formula
P = 2L + 2w
Substitution
74 = 2L + 2(L/2 + 4)
Simplification
74 = 2L + L + 8
74 = 3L + 8
74 - 8 = 3L
3L = 66
L = 66/3
L = 22
w = 22/2 + 4
w = 11 + 4
w = 15
. Let A = (−2, 4) and B = (7, 6). Find the point P on the line y = 2 that makes the total distance AP + BP as small as possible.
Answer:
P(1,2)
Step-by-step explanation:
There are 2 points.
A(-2,4) and B(7,6)
the point P on the y=2 can also represented as P(x,2)
We can use the distance formula to find the distances AP and BP
[tex]\text{dist} = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
for AP: A(-2,4) and P(x,2)
[tex]AP = \sqrt{(-2 - x)^2 + (4 - 2)^2}[/tex]
[tex]AP = \sqrt{(-2 - x)^2 + 4}[/tex]
[tex]AP = \sqrt{(-1)^2(2 + x)^2 + 4}[/tex]
[tex]AP = \sqrt{(2 + x)^2 + 4}[/tex]
for BP: B(7,6) and P(x,2)
[tex]BP = \sqrt{(7 - x)^2 + (6 - 2)^2}[/tex]
[tex]BP = \sqrt{(7 - x)^2 + 16}[/tex]
the total distance AP + BP will be
[tex]\sqrt{(2 + x)^2 + 4}+\sqrt{(7 - x)^2 + 16}[/tex] (plot is given below)
Our task is to find the value of x such that the above expression is small as possible. (we can find this either through plotting or differentiating)
If you plot the above equation, the minimum point of the curve will be clearly visible, and it will be at x = 1. Hence, the point P(1,2) is such that the total distance AP + BP is as small as possible.
The point P that makes the total distance AP + BP smallest on the line y=2 is given by the x-coordinate of the midpoint of A and B because the shortest distance is in a straight line. Therefore, the point P is (2.5, 2).
Explanation:To find the point P on the line y = 2 that makes the total distance AP + BP the smallest, you need to recall that the shortest distance between two points is a straight line. So, ideally, we want to find a point P (x,2) that is on the same vertical line (or x-coordinate) that intersects the line AB at the midpoint.
Step 1: Find the midpoint of A and B. The midpoint M is obtained by averaging the x and y coordinates of A and B: M = ((-2+7)/2 , (4+6)/2) = (2.5, 5).
Step 2: Since line y = 2 is horizontal, the x-coordinate of our point P will stay the same with the midpoint x-coordinate. Therefore, P has coordinates (2.5, 2).
So, the point on the line y = 2 that makes the total distance AP + BP as small as possible is P (2.5, 2).
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How many possible 4-digit combinations are there with the numbers 2, 3, 4, 5, 6, 7, 8, and 9 if none of the numbers appear more than once (i.E. 2343, 2333, 2323, etc.)?
Answer:
[tex]1680[/tex]
Step-by-step explanation:
we need a 4-digit number from the numbers [tex]2,3,4,5,6,7,8\ and\ 9[/tex] (without repetition ).
possible number at thousand place [tex]=8[/tex]
Possible numbers at hundred place[tex]=8-1=7[/tex]
Possible numbers at [tex]10^{th}[/tex] place [tex]=7-1=6[/tex]
possible number at unit place [tex]=6-1=5[/tex]
So total possible numbers
[tex]=8\times7\times6\times5\\=1680[/tex]
Other method :
We are taking [tex]4[/tex] numbers out of [tex]8[/tex] and here order matters so we will use permutation.
Total possible numbers [tex]=^8P_{4}[/tex]
[tex]\frac{8!}{(8-4)!}\\ =\frac{8!}{4!}\\ =8\times7\times6\times5\\=1680[/tex]
An airline has six flights from New York to California and seven flights from California to Hawaii per day. If the flights are to be made on separate days, how many different flight arrangements can the airline offer from New York to Hawaii?
a) 6*7=42
b) 6+7=13
c) 67 = 279936
d) 76 = 117649
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
Number of flights from New York to California = 6
Number of flights from California to New York = 7
Since if the flights are to be made on separate days,
So, they are independent events.
So, the number of different flight arrangements that can be made offer from New York to Hawaii would be
[tex]6\times 7\\\\=42[/tex]
Hence, Option 'a' is correct.
This is a Mathematics problem about combinations, specifically calculating the total number of possible flight arrangements from New York to Hawaii, given the number of flights per day on two separate routes. The answer is found by multiplying the number of flights from New York to California (6) by the number of flights from California to Hawaii (7), which equals 42 arrangements.
Explanation:The subject of this question is Mathematics, specifically involving the concept of combinations and arrangements. The total number of flight arrangements from New York to Hawaii can be calculated by simply multiplying the number of flights from New York to California by the number of flights from California to Hawaii. Therefore, the correct answer would be a) 6*7=42.
Conceptually, this is because for each of the 6 flights from New York to California, there are 7 possible continuing flights to Hawaii. To find all possible combinations, you would multiply the two numbers together. Through visualization, this could be seen as having 6 'branches' from New York to California, then 7 'branches' from California to Hawaii for each initial branch, giving a total of 42 possible routes.
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to prove that triangle age and triangle old are congruent by sas what other information is needed
Answer:
Congruency of triangle by SAS rule.
Step-by-step explanation:
We have to prove that [tex]\triangle AGE \text{ and } \triangle OLD[/tex] are congruent to each other by SAS congruency rule.
Thus, we need the following information to do so:
A pair of equal corresponding side.An equal pair of equal corresponding angle.A second pair of equal corresponding side.Corresponding sides are:
AG and OLGE and LDAE and ADCorresponding angles are:
[tex]\angle AGE \text{ and } \angle OLD\\\angle GEA \text{ and } \angle LDO\\\angle GAE \text{ and } \angle LOD[/tex]
John weighs three times as much as Karen. Two times John's weight plus Karen's weight is 875 pounds. How much does John weigh? How much does Karen weigh?
Answer:
John- 375
Karen- 125
Step-by-step explanation:
Answer 1...
j =3k
2j + k = 875
substituting the first eqn into the 2nd
2(3k) + k = 875
6k+ k =875
7k = 875
k =875/7 =125
thus j = 3(125) =375
Answer:john weighs 375 pounds.
Karen weighs 125 pounds
Step-by-step explanation:
Let x represent the weight of John.
Let y represent the weight of Karen.
John weighs three times as much as Karen. This means that
x = 3y
Two times John's weight plus Karen's weight is 875 pounds. This means that
2x + y = 875 - - - - - - - -1
Substituting x = 3y into equation 1, it becomes
2 × 3y + y = 875
6y + y = 875
7y = 875
y = 875/7 = 125
Substituting y = 125 into x = 3y. It becomes
x = 3 × 125 = 375
Natalie visits a grocery store to buy tomatoes. The cost of tomatoes is $26. She is remitted the bill and received $4 in change from the cashier. Write the equation to find how much she paid the cashier? Let m equal amount she paid
Answer:
m-4=26
Step-by-step explanation: I guess and feel like this is correct for some reason
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?A. 5B. 6C. 7D. 8E. 9
Answer: The answer is 6
Step-by-step explanation: this is a combination because it is without repetition.
3!/(3-2)!
(3x2x1)/1!
6/1 = 6
So the answer is 6 different ways
A tank in the shape of a right circular cone has height 12 feet and base radius 4 feet. The tank is inverted, with its vertex pointing down and base at the top. The tank contains a liquid with weight density 63 pounds per cubic foot, but is filled to a depth of 8 feet only. Set up, but DO NOT EVALUATE, an integral for the work (in foot-pounds) required to pump all the liquid present to a height one foot over the top of the tank.
Answer:
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
Step-by-step explanation:
Set up cartesian axis (x and y) to the system.
Let y axis as the line of the centre of the cone, passing through its vertex and the centre of it's circular base. The x axis could be the 90 degree line to the y axis that passes the vertex. So the origin (0,0) is at the vertex.
I'm this setup , looking it as if we are looking it in 2 dimension, we'll see that there is a signature straight line on the x-y plane, which this line will form the cone as it revolute around the y-axis
Find the equation of the line:
Using height 12 and radius base 4, we can get the slope of the line
m = 12/4 = 3
It passes through origin, so the y-intercept is 0
Hence, y = 3x
Since the volume revolves around y-axis, we use the equation volume of revolution around y-axis
V = int(πx^2,a,b)
(Definite integration of πx^2 with lower boundary a and upper boundary b
Since y=3x
x = y/3
For this que
V = int(π(y/3)^2, 0, 8)
(Definite integration of π(y/3)^2 with lower boundary 0 and upper boundary 8)
12) Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long. How many more hours of television can he watch? Set up an equation and solve. A) 2.5x = 4; Oliver can watch 1.6 more hours this week. B) x + 1 + 1.5 = 4; Oliver can watch 1.5 more hours this week. C) x + 4 = 1 + 1.5; Oliver can watch 1.5 more hours this week.
Answer:
B. Oliver can watch TV for 1.5 hours more this week.
Step-by-step explanation:
Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long.
So he has already finished 2.5 hours of watching . He can watch only for 4 hours for the total week.
Let x be the number of more hours for which he can watch television.
Then ,
x + 1 + 1.5 = 4
x + 2.5 = 4
x = 4 - 2.5
x = 1.5 hours.
So Oliver can watch television for at most 1.5 hours for the rest of the week.
Then the correct option is B.
Estimate 3.49x 7.508 by first rounding each number to the nearest whole number. Give your estimate as a whole number.
Answer:
24
Step-by-step explanation:
3.49 to the nearest whole number is 3
7.508 to the nearest whole number is 8
Multiplying both will yield 3 * 8 = 24
Although it might be mistaken that 3.49 could be approximated to 4, this is absolutely wrong. This is because we round up all values 5 and above after the decimal to 1 while we round down all values less than 5 after the decimal to 0.
Hence be it 3.4999, since it is less than 5, it is rounded as 3 to the nearest whole number digit
When analyzing related data variables, how can one tell which one is the independent variable and which one is the dependent variable?
Answer:
Dependent and independent Variable.
Step-by-step explanation:
Dependent and independent Variable.
The two variables in an experiment are independent and dependent variable. Usually, the dependent variable is denoted by y and the independent variable a re denoted by [tex]x_i[/tex]The dependent variable depends on independent variable in an experiment and thus cannot be controlled.On the other hand we can change or control the independent variables to test effect on dependent variable.As the independent variable are changed, we observe corresponding changes in the dependent variable.Example: Let money spend be the dependent variable. It depends on an independent variable of shopping. We may control or change or shopping habits to see the changes in the money spent. Money spent totally depends in the amount f shopping done.A group of friends decided to rent a house in Aspen, Colorado for a week of skiing. They each had to chip in $70 for the week’s lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $14. What was the rent for the week?
Answer:
70/5
Step-by-step explanation:
70/3 and then try 70/4 and then 70/5
The total rent for the week was $840, based on the given conditions of per person cost and the price decrease with additional participants.
Explanation:The subject of this question is Mathematics, and this is a problem ideally pitched at high school level. It involves constructing equations from the given information to solve the problem.
Let's begin by determining the amount of people who went on the trip initially. We'll call them 'n'. The cost per person on the trip was $70, so that the total cost of the trip is $70n.
Now, if they had persuaded three more people to go (n + 3), the cost per person would've dropped by $14 to $56 which, multiplied by the new total of attendees would still be equal to the total cost of the trip ($56(n + 3)).
As such, we build the equation $70n = $56(n + 3). Here's the breakdown and solving of the equation: $70n = $56n + $168.
Subtracting $56n from both sides gives $14n = $168. Dividing both sides by 14 finally gives n = 12.
To find the total cost of the rent, substitute n = 12 into the equation $70n, yielding $70(12) = $840.
So, the rent for the week was $840.
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At a hardware store a tool set normally cost $80 during the sale this week the tools that cost $12 less than usual what percentage of the usual price is a savings explain or show your reasoning
15 % of usual price is a savings
Solution:
Given that tool set normally cost $80
During the sale this week the tools that cost $12 less than usual
To find: what percentage of the usual price is a savings
From given information,
Usual price of tool set = $ 80
Given that tools that cost $12 less than usual which means she saved $ 12
Savings = $ 12
To find what percentage of the usual price is a savings, we can solve by framing a expression,
Let "x" be the required percentage
Then x % of percentage is equal to savings price
x % of usual price = savings price
x % of 80 = 12
[tex]\frac{x}{100} \times 80 = 12\\\\x = \frac{12 \times 100}{80}\\\\x = 15 \%[/tex]
Therefore 15 % of usual price is a savings
Renee wants to put a fence around her Square Garden that has an area of 6500 square feet determine the perimeter of the garden to the nearest tenth of a foot
Answer:
299.3
Step-by-step explanation:
1. what is x? (picture 1 and 2)
2. What is the length of NO? (3rd picture)
3. If LB = 6 and LN = 2x+5, what is x? (fourth picture)
Answer:
Part 1) [tex]x=6[/tex]
Part 2) [tex]x=5,75[/tex]
Part 3) [tex]NO=80\ units[/tex]
Part 4) [tex]x=3,5[/tex]
Step-by-step explanation:
Part 1) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
GH=FE
substitute the given values
[tex]2x+10=22[/tex]
solve for x
subtract 10 both sides
[tex]2x=22-10[/tex]
[tex]2x=12[/tex]
Divide by 2 both sides
[tex]x=6[/tex]
Part 2) Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
FG=EH
substitute the given values
[tex]4x+5=28[/tex]
solve for x
subtract 5 both sides
[tex]4x=28-5[/tex]
[tex]4x=23[/tex]
divide by 4 both sides
[tex]x=5,75[/tex]
Part 3) What is the length of NO?
step 1
Find the value of x
we know that
In a parallelogram opposites sides are congruent and parallel
In this problem
NO=ML
substitute the given values
[tex]4x+20=2x+50[/tex]
solve for x
Group terms
[tex]4x-2x=50-20[/tex]
[tex]2x=30[/tex]
Divide by 2 both sides
[tex]x=15[/tex]
step 2
Find the value of NO
we have that
[tex]NO=4x+20[/tex]
substitute the value of x
[tex]NO=4(15)+20=80\ units[/tex]
Part 4) we know that
The diagonals in a parallelogram bisect each other
so
LB=BN
LN=LB+BN ----> by addition length postulate
LN=2LB
substitute the given values
[tex]2x+5=2(6)[/tex]
solve for x
[tex]2x+5=12[/tex]
subtract 5 both sides
[tex]2x=12-5[/tex]
[tex]2x=7[/tex]
Divide by 2 both sides
[tex]x=3,5[/tex]
Diane loves coasters that dip into tunnels during the ride.Her favorite coaster is modeled by h(t)=2t +23t-59t+24. Using rational route theorem, what are the possible rational zeros for the function
Answer:
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2
Step-by-step explanation:
I believe that there is an error in the function with the exponents, it must be:
[tex]h(t) = 2t^{3} + 23t^{2}+59t+24[/tex]
If this is the function that you need, then we must use the rational zero theorem. It says that if a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Thus
In this case the constant term is 24 and then
p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
The factor of the leading coefficient is 2, thus
q = ±1, ±2
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2