Hey there, we are given quite a lot of information in this problem. First of all, let's make an equation.
y = x - 22
where y = student's age
where x = instructor's age
this equation is correct because x(instructor) - 22 will yield the student's age (y).
If the instructor were 44 years old, the student would be 22 years old.
y = 44 - 22
y = 22
If the instructor were 66 years old, the student would be 44 years old.
y = 66 - 22
y = 44
You are 5 feet tall. What is your height in meters (m)?
Answer:
1.524
Step-by-step explanation:
Answer:
1.52 meters
Step-by-step explanation:
Sarah has 25 coins that are dimes and nickels. Together they total $2.00. How many of each type does she have?
Answer:
15 dimes and 10 nickels
Step-by-step explanation:
15 dimes because 15 multiplied by 10 cents is $1.50
10 nickels because 10 multiplied by 5 cents is $0.50
15 x 0.10 = 1.50 10 x 0.50 = 0.50
0.50 + 1.50 = 2.00
Answer:
15 dimes 10 nickles
Hope this helps!
Which of the following sets represents the range of the function shown?
Answer:
{0, -1, 11, 13 }
Step-by-step explanation:
the range of the function are the corresponding values of y from the set of points, in ascending order, that is
{0, -1, 11, 13 }
Answer:
Step-by-step explanation:
The range is the set of y values of the function.
{0, -1, 11, 13]
What is the surface area of a cone with a 6 in. diameter and a length (slant height) of 8 in.?
The formula of a surface area of a cone:
[tex]SA=pi rl+\pi r^2[/tex]
r - radius
l - slant height
We have the diameter d = 6 in and a slant height l = 8 in.
[tex]d=2r\to r=6in:2=3in[/tex]
Substitute:
[tex]SA=\pi(3)(8)+\pi(3^2)=24\pi+9\pi=\boxed{33\pi\ in^2}[/tex]
Apply the distributive property to factor out the greatest common factor.
75+20=
Answer:
5(15+4)
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values 75 and 20. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:
75: 1,3,5,15,25, 75
20: 1, 2, 4, 5, 10, 20
Both have 5 and this is the GCF. So we write the expression int he form 5(___+___). We divide each term by 5 to find the corresponding factor.
75/5= 15
20/5=4
5(15+4)
Answer:
5(15+4)
Step-by-step explanation:
5
15+
and (4)
add them all together.
Today lan wants to run less than 7/12 mile.Write a fraction with a denominator of 4 to represent a distance that is less than 7/12 mile.
Answer:
the answer is 1/4 because 7/12 is larger than 1/2 but 1/4 is 2x smaller
Step-by-step explanation:
PLEASE HELP ASAP! WILL MARK BRAINLIEST
hoping to be named salesperson of the month, JJ called the names from 5/8 of a page of the phone book last week. this week, he called the people listed on another 5/8 of a page on the same phonebook. how many pages worth of people did JJ call in all?
Answer:
he called 1 page and 1/4
Step-by-step explanation: so 5/8+5/8=10/8 sooo.. simpify that and get 1 1/4
1 1/4
Answer:
11 4/5
(I think that is the answer)
Hope I helped :)
In a rectangle, the ratio of the length to the width is 5 : 2. The length of the rectangle is 13.875 feet greater than the width. What are the perimeter and the area of the rectangle?
Answer:
Perimeter = 64.75 ft
Area = 213.91 ft
Step-by-step explanation:
13.875 ÷ 3 = 4.625
4.625 x 5 = 23.125 ft (This is the length of the rectangle)
4.625 x 2 = 9.25 ft (This is the width of the rectangle)
(23.125 x 2) + (9.25 x 2) = 64.75 ft (Perimeter)
23.125 x 9.25 = 213.90625 ft, or 213.91 ft if rounded to 2 d.p (Area)
The perimeter of the rectangle is approximately 64.75 feet and the area is approximately 213.91 square feet.
How to solve for the area and perimeter[tex]\[L = W + 13.875\][/tex]
We can use these two equations to solve for the values of \(L\) and \(W\).
First, let's use the ratio to set up an equation:
[tex]\[\frac{L}{W} = \frac{5}{2} \implies L = \frac{5}{2}W\][/tex]
Next, substitute this expression for L into the second equation:
[tex]\[\frac{5}{2}W = W + 13.875\][/tex]
Solving for w
[tex]\[\frac{3}{2}W = 13.875\][/tex]
[tex]\[W = \frac{2}{3} \times 13.875\][/tex]
[tex]\[W = 9.25\][/tex]
Now, use this value of \(W\) to find the length \(L\):
[tex]\[L = \frac{5}{2} \times 9.25 = 23.125\][/tex]
Now that we have the dimensions, we can calculate the perimeter and area:
1. perimeter of a rectangle with length \(L\) and width \(W\) is given by:
[tex]\[P = 2(L + W)\][/tex]
Substituting the values:
[tex]\[P = 2(23.125 + 9.25) \approx 64.75 \text{ feet}\][/tex]
2. Area of a rectangle is given by:
[tex]\[A = L \times W\][/tex]
Substituting the values:
[tex]\[A = 23.125 \times 9.25 \approx 213.91 \text{ square feet}\][/tex]
So, the perimeter of the rectangle is approximately 64.75 feet and the area is approximately 213.91 square feet.
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Harper knows he is 50 yards from school. The map on his phone shows that the school is 34 inch from his current location. How far is Harper from home, if the map shows the distance as 3 inches? Enter your answer in the box. yards
Answer:
4.4 yd
Step-by-step explanation:
Scale = 50 yd:34 in
Distance from home = 3 × 50/34
Distance from home = 4.4 yd
S is a geometric sequence. (Square root x-1),1 and (square root x+1) are the first three terms of s. Find the value of x.
Answer:
x = ± [tex]\sqrt{2}[/tex]
Step-by-step explanation:
given the 3 terms of a geometric sequence
[tex]\sqrt{x-1}[/tex], 1, [tex]\sqrt{x+1}[/tex], then the common ratio r
r = [tex]\frac{\sqrt{(x+1)} }{1}[/tex] = [tex]\frac{1}{\sqrt{(x-1)} }[/tex] ( cross- multiply )
[tex]\sqrt{(x+1)(x-1)}[/tex] = 1 ( square both sides )
(x + 1 )(x - 1 ) = 1 ← expand factors on left side )
x² - 1 = 1 ( add 1 to both sides )
x² = 2 ( take the square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
The value of x is ±[tex]\sqrt{2}[/tex].
What is a Geometric Sequence?It is a sequence, where the ratio of two consecutive terms in a sequence are constant.It is a finite or infinite sequence.Geometric Sequence G is given by: G = a, ar², ar³,..... (a = first term; r = constant ratio)Given:
Geometric Sequence with first three terms.
[tex]\sqrt{x-1},1, \sqrt{x+1[/tex]
We have to find the value of x.
Now, if the given sequence is geometric then we can find the common ratio of the sequence.
The common ratio is given by:
r = [tex]\frac{1}{\sqrt{x-1} }[/tex] and r = [tex]\frac{\sqrt{x+1} }{1}[/tex]
Now, we can equate the both the values of r to solve for the value of x.
[tex]\frac{\sqrt{x+1} }{1} = \frac{1}{\sqrt{x-1} }[/tex]
Now, multiplying the numerator on both sides by [tex]\sqrt{x-1}[/tex], we get:
[tex]\sqrt{x+1} \sqrt{x-1} =1[/tex]
[tex]\sqrt{(x-1)(x+1)}=1[/tex]
[tex]\sqrt{x^2-1} =1[/tex]
Now, squaring on both sides of the equation, we get:
⇒ x² - 1 = 1
⇒ x² = 2
Now, taking square root on both the sides, we get:
⇒ x = ±[tex]\sqrt{2}[/tex]
Therefore, for a given geometric sequence the value of x will be ±[tex]\sqrt{2}[/tex].
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How do you solve this?
Answer:
Multiply 60 by .40
60 * .40 = 24
Answer is B
Step-by-step explanation:
Mr.carter and ms.torres need two busses to drive their classes to the amusement park. Each class needs money to rent a bus and $20 to tip the driver.the two classes together raised $240 how much money can they spend on each bus rental?
Answer:
$100
Step-by-step explanation:
if $20 is needed for one bus tip, then $40 is needed for the two buses that the teachers will need
so $240 - $40 = $200 to spend on bus rentals
since there are two buses, the $200 needs to be halved
therefore, each bus rental is $100
Dawn is verifying the accuracy of her paycheck. She earns $12 an hour and works 40 hours each week. Herr biweekly deductions are Social Security 6.2%. Medicare 1.45%, federal withoutholding tax $73.25, state withholding tax $22.50, and health insurance $37.47. What is her net pay if she is paid biweekly?
Answer: $ 753.34
Step-by-step explanation:
Since, here She earns $12 an hour and works 40 hours each week.
Therefore, her earning in two weeks = 2 × 12 × 40 = $ 960
Now, Her biweekly deductions are Social Security 6.2%. Medicare 1.45%, federal with out holding tax $73.25, state withholding tax $22.50, and health insurance $37.47.
Therefore, Her total deduction = (6.2+1.45)% of 960 + (73.25+22.50+37.47)= 73.44+133.22= 206.66
Since, Net pay is the amount of payee after deductions have been taken from the his gross pay.
Therefore, Net pay = total amount - total deduction = 960 - 206.66 = $ 753.34
Her net pay if she is paid biweekly is $ 753.34.
we have given that,
She earns $12 an hour and works 40 hours each week.
Therefore, her earning in two weeks,
= 2 × 12 × 40
= $ 960
Her biweekly deductions are Social Security 6.2%. Medicare 1.45%, federal with out holding tax $73.25, state withholding tax $22.50, and health insurance $37.47.
Therefore,
[tex]Her total deduction = (6.2+1.45)% of 960 + (73.25+22.50+37.47)\\\\\\\\Her total deduction= 73.44+133.22\\ \Her total deduction= 206.66[/tex]
What is the net pay amount formula ?Net pay is the amount of payee after deductions have been taken from the his gross pay.
Net pay = total amount - total deduction
Therefore by using formula,
Net pay= 960 - 206.66
Net pay = $ 753.34
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can anyone help me with number 10??
Answer:
y=−4/3x+10
Step-by-step explanation:
Find the negative reciprocal of the slope of the original line and use the slope-intercept form y=mx+b to find the line perpendicular to 3x−4y=−2.
what is the image of the point (-6,2) after a 90 degree counterclockwise rotation
Will mark brainliest! :D
Answer: 137 + 4(n-1)
Step-by-step explanation:
137 + 4(n-1)
Okay, let's test this starting with week 1:
137 + 4(1-1)
137 + 4*0
137, which is correct because she starts with 137.
Week 2:
137 + 4 (2-1)
137 + 4 * 1
137 + 4
141
Alright, let's see if it is correct if we do week 5:
137 + 4 (5-1)
137 + 4(4)
137 + 16
153
To know that 153 is right we could do 137 + 4 + 4 + 4 + 4, which equals 153.
FAST!! the hcf of 2 numbers is 98 and there LCM is 2352..the sum of their numbers may be
Answer:
Step-by-step explanation:
I hope it will help you
Attachment
Complete the statement about the tables below. Then, choose a rule for each. x y 0 5 1 7.5 2 11.25 This table represents a(n) relationship. Rule: x y 0 -6 1 12 2 30 This table represents a(n) relationship. Rule:
The first table represents an exponential relationship.
Rule: [tex]\(y = 5 \times 1.5^x\)[/tex]
The second table represents a linear relationship.
Rule: [tex]\(y = 6x - 6\)[/tex]
The first table represents an exponential relationship.
Rule: The rule for the first table can be expressed as [tex]\(y = 5 \times 1.5^x\)[/tex]. Each (y) value is obtained by multiplying the previous (y) value by 1.5.
The second table represents a linear relationship.
Rule: The rule for the second table can be expressed as [tex]\(y = 6x - 6\)[/tex]. Each (y) value is obtained by multiplying the corresponding (x) value by 6 and then subtracting 6.
Each year, thousands of people visit Yellowstone national park. Audiotapes for visitors include interviews with early settlers and information about geology, wildlife, and activities of the park. The revenue r(x) from the sale of x tapes is r(x)=9.5x. Suppose that the function for the cost of manufacturing x tapes is c(x)=0.8x+1940.
What function could be used to find the profit on x tapes?
a. Write the profit function.
b.find the profit on 500, 1000, and 5000 tapes.
c. Check by finding the revenue and the cost for each number of tapes and subtracting to find profit
Answer: p(x) = 8.7x - 1940
p(500) = $2410
p(1000) = $6760
p(5000) = $41,560
Step-by-step explanation:
p(x) = r(x) - c(x)
= 9.5x - (0.8x + 1940)
= 9.5x - 0.8x - 1940
= 8.7x - 1940
**********************************************************************
p(500) = 8.7(500) - 1940
= 4350 - 1940
= 2410
p(1000) = 8.7(1000) - 1940
= 8700 - 1940
= 6760
p(5000) = 8.7(5000) - 1940
= 43,500 - 1940
= 41,560
***************************************************************************
p(500) = r(500) - c(500)
= 9.5(500) - [0.8(500) + 1940]
= 4750 - (400 + 1940)
= 4750 - 2340
= 2410
p(1000) = r(1000) - c(1000)
= 9.5(1000) - [0.8(1000) + 1940]
= 9500 - (800 + 1940)
= 9500 - 2740
= 6760
p(5000) = r(5000) - c(5000)
= 9.5(5000) - [0.8(5000) + 1940]
= 47500 - (4000 + 1940)
= 47500 - 5940
= 41,560
solve the inequality algebraically. express your answer using interval or set notation. graph the solution set. -5 less than or equal to 4 - 3x less than or equal to 2
Step-by-step explanation:
This ≤ inequality sign means:
Less than/Equal toNo more thanAt mostMaximum of-5 ≤ 4
And then:
-3x ≤ 2
OR:
-5 ≤ 4 -3x ≤ 2
Hi!!! Sorry, I didn't know if they were suppose to be together or separate, so I just did it both ways!!! :) Really sorry if I am wrong...
20.8 is 32% of what number
[tex]\begin{array}{ccc}20.8&-&32\%\\x&-&100\%\end{array}\qquad\text{cross multiply}\\\\32x=(20.8)(100)\\\\32x=2080\qquad\text{divide both sides by 32}\\\\\boxed{x=65}[/tex]
Answer: 20.8 id 32% of 65.The number that 20.8 is 32% of is 65, achieved by setting up an equation representing 32% of a number equal to 20.8 and solving for that number.
Explanation:The question is asking you to find a number such that 32% of it equals 20.8. You represent this situation mathematically as '32/100 * X = 20.8', where 'X' is the number we need to find. Solving for 'X' gives us 'X = 20.8 ÷ (32/100)'. Performing this operation gives us 'X = 65'.
So, 20.8 is 32% of 65, which is the solution to the problem. The primary focus here is understanding percentages and how to solve these types of questions.
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The length of a rectangle is 1 less than twice the width.
The area of the rectangle is 28 square feet.
Which equation represents the situation?
What is the length of the rectangle?
[tex]w-width\\2w-1-length\\w(2w-1)=2w^2-w-the\ area\\28\ ft^2-the\ area\\\\\text{The equation:}\\\\2w^2-w=28\qquad\text{subtract 28 from both sides}\\\\2w^2-w-28=0\\\\2w^2-8w+7w-28=0\\\\2w(w-4)+7(w-4)=0\\\\(w-4)(2w+7)=0\iff w-4=0\ \vee\ 2w+7=0\\\\w-4=0\qquad\text{add 4 to both sides}\\\boxed{w=4}\\\\2w+7=0\qquad\text{subtract 7 from both sides}\\2w=-7\qquad\text{divide both sides by 2}\\w=-3.5<0\\\\\text{The length:}\ 2(4)-1=8-1=7\\\\Answer:\ \boxed{\text{The length is equal 7\ ft}}[/tex]
Answer:
equation = 2w^2- w- 28 =0
length =7
Solve for m.
m−14.6=9.74
4.86
23.34
24.34
25.34
Answer:
the correct answer is 100% C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
PLEASE help with number 5!!
Answer:
5/12
Step-by-step explanation:
1. Convert 1/4 to 3/12, then convert 1/3 to 4/12
2. Then add 3/12 and 4/12 together, which would be 7/12
3. Then subtract 12/12 by 7/12 which would be 5/12
So, 5/12 is your answer.
Hope this helps
how to solve the algebraic expression 25=5/3(d+5/8)
Answer:
Alright well solve for d by cross multiplying
Exact form: d = 115/8
Decimal form: d = 14.375 Hope this helps have a nice day : )
Step-by-step explanation:
4z
27
+x5
y14
If x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)?
By analyzing the equation and using provided options, we find that the right values for the digits x, y, and z are 1, 2, and 3 respectively. When multiplied together, the product (x)(y)(z) equals 6.
Explanation:The mathematical problem you've presented is akin to a simple addition of numbers, but with a twist: the digits x, y, and z each represent different unknown digits. Our task is to determine the value of the product (x)(y)(z) given the vertical addition:
4zLooking at the addition, we can see that when we add the second digit of the second row (2) with the first digit of the third row (x), the result must be a digit with a 1 carried over because there is a 1 in the hundred's place of the result. That means 2 + x has to be equal to 10 or 11 (since x is a digit, the highest value for x could be 9).
Using the option provided (d) x. 1, y. 2, z. 3, we can see that the column with z's would sum to 7 (4z), the column with x's would sum to 11 (since 1 + x = 11, x = 1), and the column with y's would sum to 14 (since y would then be 2) which fits the pattern of the problem provided. Therefore, the values for x, y, and z are 1, 2, and 3 respectively.
The value of (x)(y)(z) is thus 1 × 2 × 3 = 6.
Final answer:
To find the value of (x)(y)(z), we need to solve the equation 4z/27 + x5/y14 = 0. By substituting different values for x, y, and z, we find that (x)(y)(z) = 6.
Explanation:
To find the value of (x)(y)(z), we need to solve the given equation:
4z/27 + x5/y14 = 0
Since x, y, and z each represent a different digit from 0 to 9, we can try different values to solve for (x)(y)(z).
Let's start with the first term: 4z/27. The only possible value for z is 2, because 4z/27 must give us a rational number. So, let's substitute z = 2 into the equation:
4(2)/27 + x5/y14 = 0
8/27 + x5/y14 = 0
Next, let's solve for the second term: x5/y14. To make this term equal to 0, we can set x = 1 and y = 3. Substituting these values into the equation:
8/27 + 15/314 = 0
Now, let's find the value of (x)(y)(z) = (1)(3)(2) = 6.
What is the value of X?
If all angles have the same measure, then this is an equilateral triangle.
Therefore we have the equation:
4x - 30 = 3x - 5 add 30 to both sides
4x = 3x + 25 subtract 3x from both sides
x = 25
Check:
|AB| = 3x - 5 → |AB| = 3(25) - 5 = 75 - 5 = 70
|BC| = 2x + 20 → |BC| = 2(25) + 20 = 50 + 20 = 70
|AC| = 4x - 30 → |AC| = 4(25) - 30 = 100 - 30 = 70
CORRECT :)
Answer: x = 25Using a calculator and the formula, calculate the APR. Choose the correct answer.Bob Businessman offers credit at 20% interest per year.
Answer:21.9
Step-by-step explanation:i just finished this question on a test and got it right hope this helps
Which triangle is not labeled correctly
Answer:
Step-by-step explanation:
What are the triangles? Did you forget to attach a picture?
jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is 1/15. The theoretical probability of rolling a 2 is 1/6 What could Jamie do to make his experimental results more closely match the theoretical probability?
Answer:
Answer is to increase trials
Step-by-step explanation:
Theoretical Probability is what it is expected to happen whereas Experimental Probability is what actually happens.
What Jamie should take into serious consideration is that Experimental probability gets gradually closer to theoretical probability as the number of trials increases.
In other words, Jamie needs to increase the number of trials in order to match experimental and theoretical probabilities every time more and more.
Answer: letter A
to increase the number of trials
Step-by-step explanation: