Final answer:
Jada's speed (⅔ mile per minute) is three times faster than her cousin's speed (⅔ mile per minute); thus, Jada is moving faster.
Explanation:
To determine who is moving faster between Jada and her cousin, we need to calculate their swimming speeds and compare them. Speed can be calculated by dividing the distance by the time it takes to cover that distance.
Jada's Speed:
Jada swims 2 miles in 12 minutes. To find her speed, we use the formula:
Speed = Distance ÷ Time
Speed = 2 miles ÷ 12 minutes = ⅔ mile per minute
Jada's Cousin's Speed:
Jada's cousin swims 1 mile in 24 minutes. Using the same formula:
Speed = 1 mile ÷ 24 minutes = ⅔ mile per minute
Comparison and Result:
Jada's speed is ⅔ mile per minute, whereas her cousin's speed is ⅔ mile per minute. Jada is swimming at a higher speed because she covers more distance in less time compared to her cousin. Specifically, she swims three times faster, evidenced by comparing their speeds:
Jada's speed ÷ Cousin's speed = ⅔ mile per minute ÷ ⅔ mile per minute = 3
Therefore, Jada is moving three times faster than her cousin.
Given f(x) = 364-27, what is the value of f(16)
Answer:
f(16)=337
Step-by-step explanation:
YOUR TURN
9. Out of the 25 students in Mrs. Green's class, 19 have a per. Wh
of the students in Mrs. Green's class have a pet?
Answer:
[tex]\frac{19}{25}[/tex] or [tex]76%[/tex]
Step-by-step explanation:
As a fraction: [tex]\frac{19}{25} \\[/tex] it can't be simplified further
As a percentage: [tex]\frac{19}{25} =0.76[/tex]
1. In quadrilateral QUAD shown below, point R is the midpoint of diagonal QA. What are
the coordinates of point Q?
R(-2, 10)
A (12,6)
A. (-16,14)
B. (-12, 16)
C. (-14,4)
D. (-7,2)
Answer:
Option A. (-16,14)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
In this problem we have that
[tex]point\ Q(x1,y1)\\point\ A(x2,y2)[/tex]
[tex](-2,10)=(\frac{x1+12}{2},\frac{y1+6}{2})[/tex]
so
[tex]\frac{x1+12}{2}=-2[/tex] ---> [tex]x1=-4-12=-16[/tex]
[tex]\frac{y1+6}{2}=10[/tex] ---> [tex]y1=20-6=14[/tex]
therefore
The coordinates of point Q are (-16,14)
The coins in Diego’s pocket are worth 150% of a dollar. How much are they worth (in dollars)?
Answer:
In Diego’s pocket are worth $1.5.
Step-by-step explanation:
Given:
The coins in Diego’s pocket are worth 150% of a dollar.
Now, to find the worth in dollars in Diego's pocket.
So, as given the coins in Diego’s pocket are worth 150% of a dollar.
That means 150% of $1. As a dollar expresses 1$.
Thus, 150% of 1$.
[tex]=\frac{150}{100} \times 1[/tex]
[tex]=1.5\times 1[/tex]
[tex]=\$1.5.[/tex]
Therefore, in Diego’s pocket are worth $1.5.
Diego's coins are worth 150% of a dollar, which means they are worth $1.50. This was calculated by converting 150% to a decimal (1.50) and multiplying it by 1 dollar.
The question involves calculating the value of coins in terms of dollar amounts, which falls under the subject of Mathematics, specifically dealing with percentages and conversion of values.
Diego has coins in his pocket worth 150% of a dollar. To find out how much this is in dollars, we need to convert the percentage to a decimal by dividing by 100, which gives us 1.50. Therefore, the coins in Diego's pocket are worth $1.50. This is because 150% of 1 dollar is 1.5 times 1, which equals 1.5 or $1.50.
Remember, in math, percentages over 100% mean that you have more than the whole. So, 150% represents 1 whole (100%) plus half of another whole (50%), which in terms of dollars, translates to $1.50.
which of the following is a solution of x^2+4x+6
Answer:
Option 1) [tex]x=-2+i\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +4x+6=0[/tex]
so
[tex]a=1\\b=4\\c=6[/tex]
substitute in the formula
[tex]x=\frac{-4\pm\sqrt{4^{2}-4(1)(6)}} {2(1)}[/tex]
[tex]x=\frac{-4\pm\sqrt{-8}} {2}[/tex]
Remember that
[tex]i=\sqrt{-1}[/tex]
so
[tex]x=\frac{-4\pm i\sqrt{8}} {2}[/tex]
[tex]x=\frac{-4\pm2i\sqrt{2}} {2}[/tex]
[tex]x=-2\pm i\sqrt{2}[/tex]
The solutions are
[tex]x=-2+i\sqrt{2}[/tex]
and
[tex]x=-2-i\sqrt{2}[/tex]
Which expressions are equivalent to 35+30s-45t35+30s−45t35, plus, 30, s, minus, 45, t?
Answer:
The correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
Step-by-step explanation:
Consider the provided expression.
[tex]35 + 30s - 45t[/tex]
Option (A): [tex]7\cdot(5+30s-45t)[/tex]
Open parenthesis.
[tex]35+210s-315t[/tex]
Which is not equal to the provided expression.
Option (B) [tex]5(7+6s-9t)[/tex]
Open parenthesis.
35+30s-45t
Which is equal to the provided expression.
Option (C) [tex](-35-30s+45t)\times (-1)[/tex]
Open parenthesis.
[tex]35+30s-45t[/tex]
Which is equal to the provided expression.
Option (D) [tex]10\times(3.5+3s-4.5)[/tex]
[tex]35+30s-45[/tex]
Which is not equal to the provided expression.
Option (E) [tex](\frac{35}{2}- 15s + \frac{45t}{2}) \cdot(-2)[/tex]
Open parenthesis.
[tex]-35+30s-45t[/tex]
Which is not equal to the provided expression.
Hence, the correct option is B. [tex]5(7+6s-9t)[/tex] and C. [tex](-35-30s+45t)\times (-1)[/tex].
A line includes the points (10,1) and (a,-5) has a slope of 1/3. What is the value of a?
For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})\ and\ (x_ {2}, y_ {2})[/tex]are two points through which the line passes.
According to the statement we have:
[tex](x_ {1}, y_ {1}) :( 10,1)\\(x_ {2}, y_ {2}) :( a, -5)\\m = \frac {1} {3}[/tex]
Substituting we have:
[tex]\frac {1} {3} = \frac {-5-1} {a-10}\\\frac {1} {3} = \frac {-6} {a-10}\\a-10 = \frac {-6} {\frac {1} {3}}\\a-10 = -18\\a = -18 + 10\\a = -8[/tex]
Thus, the value of a is -8.
Answer:
[tex]a = -8[/tex]
twice a number x,minus 19
Answer:
2x - 19
Step-by-step explanation:
"Twice a number x" means the (missing) number is called x. Write "2x" which means multiply "x" by 2.
"Minus 19" is -19.
Together, the expression is 2x - 19.
A bedroom has the shape shown. The homeowner is upgrading by putting in new crown molding. How many feet of crown molding does she need?
Answer: D.
Step-by-step explanation: Add all of the sides' lengths together. The rest of the wall beneath where "5 ft." is measures as 6 ft. Add that to the 5 ft of the rest of the wall and you'll have 11 for the whole right wall. Add 11 to 8, 10 and 12, and you'll have 41 which is close to the last choice so you're safest bet is D.
The homeowner needs 48 feet of crown molding.
Explanation:To determine how many feet of crown molding she needs, the homeowner needs to find the perimeter of the room. The room has four sides, each measuring 12 feet, so the perimeter is 4 * 12 = 48 feet. Therefore, the homeowner needs 48 feet of crown molding.
The function g is defined by g(x)=cx-3, where c is a constant. Find c if the value of g(x) at x=0.5 is equal to -1
Answer:
c = 4
Step-by-step explanation:
In g(x)=cx-3 when x is set to 0.5 , g(x)= -1.
We can solve for "c" when it is the only variable in the equation.
Substitute x for 0.5 and g(x) for -1. Isolate "c" to solve by doing reverse operations.
g(x) = cx - 3
g(0.5) = 0.5c - 3 Substitute x=0.5
-1 = 0.5c - 3 Substitute g(0.5) = -1
-1 + 3 = 0.5c - 3 + 3 Add 3 to both sides to start isolating c
2 = 0.5c
2/0.5 = 0.5c/0.5 Divide both sides by 0.5 to isolate c
4 = c Value of c
c = 4 Standard formatting puts the variable on the left side
Therefore the value of c if g(0.5)=-1 is 4.
Answer:
c = 4.
Step-by-step explanation:
Substitute the given values x = 0.5 and g(x) = -1:
-1 = c(0.5) - 3
0.5c = -1 + 3 = 2
c = 2/0.5
c = 4.
Solve the equation for g
w=gh-2gk^2
Answer:
The Answer is in the picture above
plz Mark me brainliest answer
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i dont get this plz help me
Answer:
1] Estimated cost for 1 semester=$22800
2] Total semester in 4 years=8
3] Estimated total cost for 4 years =$182400
Step-by-step explanation:
Given:-
Estimated cost per semester
Tuition fee(T) =$10000
Books(B) = $1200
Room and board(R)=$10030
Other expense(O)=$1570
Now,
1] To find the estimated cost to attend this college for 1 semester.
Answer:-
Estimated cost for 1 semester(E)= Tuition fee+Books+Room and Board+Other expense
[tex]E=T+B+R+O[/tex]
[tex]E=10000+1200+10030+1570[/tex]
[tex]Estimated\ cost\ for\ 1\ semester=22800[/tex]
Therefore estimated cost to attend this college for 1 semester = $22800
2]Each year has 2 semester. How many semester will Joe pay for if he attends for 4 years.
Answer:-
If 1 year has 2 semester, then
total semester in 4 years=[tex]2\times 4[/tex]
total semester in 4 years=8
Therefore Joe will pay for 8 semester if attends for 4 years.
3] What is the estimated total cost for Joe to attend this college for 4 years.
Estimated total cost for 4 years = Estimated total cost for 1 semester[tex]\times[/tex]8
Estimated total cost for 4 years=22800[tex]\times[/tex]8
Estimated total cost for 4 years =$182400
The sum of two consecutive integers is 131
Answer:
65 and 66
Step-by-step explanation:
x + (x+1) = 131
2x + 1 = 131
2x = 131 - 1 = 130
x = 65
x + 1 = 66
Simplify to create an equivalent expression.
8(10 - 69q) +3(-7q - 2)
Choose 1 answer:
-69q + 78
-55q + 74
-69q + 74
69q + 74
Answer:
-573q+74
Step-by-step explanation:
8(10-69q)+3(-7q-2)
80--552q-21q-6
80-573q-6
-573q+74
Answer:
the other guys i wrong completely the actual answer is −69q+74 i just did it and i am tring to help more people
Step-by-step explanation:
I need help please and thank you
Answer:
400
Step-by-step explanation:
Movies, drinks and candies are independent events and you can choose one for each.
Movie: 10 options can be selected
drinks: 5
candy: 8
All types: 10 x 5 x 8 = 400
The function c=3x-y is minimized at the vertex point of the feasible region at (4,5). What is the minimum value
(x,y)=(4,5)
c = 3x-y = 3(4) - 5 = 7
Answer: 7
Final answer:
The minimum value of the function c=3x-y at the vertex point (4,5) of the feasible region is 7.
Explanation:
The question provided by the student involves finding the minimum value of a function of two variables, given by c=3x-y, at a certain point in the feasible region. Since the minimum is achieved at the vertex point (4,5), we can directly substitute these values into the function to find the minimum value.
To calculate the minimum value of the function c=3x-y at the point (4,5), we substitute x=4 and y=5 into the equation:
c = 3×4 - 5
c = 12 - 5
c = 7
Therefore, the minimum value of the function is 7 at the vertex point (4,5).
Fill in the using table this function rule y=-10x+2
Write an equation for the line that is parallel to y =
-2x and passes through the point (0, -7).
Answer:
y=-2x-7
Step-by-step explanation:
y=-2x
y-y1=m(x-x1)
y-(-7)=-2(x-0)
y+7=-2(x)
y+7=-2x
y=-2x-7
find the scale factor.
The scale factor is 1.5. The dilation rule is : (x,y)-------(.15x,1.5y)
Step-by-step explanation:
Dilation is a transformation that maps an object to an image of the same shape as the original object to form a different size image.When a larger image is produced it's called an enlargement where as when a small image is produced, it's called a reduction.
The rule of dilation, with center as the origin follows;
(x,y)------(sx,sy) where s is the scale factor. To find the scale factor, select one of the vertices of the object and of the image at divide the coordinate of image with that of object.
Taking O(2,16) and O'(3,24), the scale factor will be;
s*2=3
2s=3
s=3/2 =1.5
or
s*16=24
16s=24
s=24/16=3/2=1.5
The scale factor is 1.5, hence the dilation rule is;
(x,y)-------(.15x,1.5y)
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Keywords: dilation, vertices, origin, scale factor, translation
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If f(x) = 9x – 8, which of the following is the inverse of f(x)?
A.
f –1(x) =
B.
f –1(x) =
C.
f –1(x) =
D.
f –1(x) =
Answer: [tex]f^{-1}[/tex] (x) = [tex]\frac{x+8}{9}[/tex]
Step-by-step explanation:
f(x) = 9x - 8 , to find the inverse of f(x) , replace f(x) with y , then the equation becomes
y = 9x - 8 , then make x , the subject of the formula ,
9x = y + 8
x = [tex]\frac{y+8}{9}[/tex]
Finally , replace x , with [tex]f^{-1}[/tex] (x) and y with x , so we have
[tex]f^{-1}[/tex] (x) = [tex]\frac{x+8}{9}[/tex]
an amount of $41,000 is borrowed for 7 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of that year, how much must be paid back?
Answer:
We must pay back US$ 64,767.70 for the loan after 7 years.
Step-by-step explanation:
1. Let's review the data given to us for answering the question:
Loan amount = US$ 41,000
Duration of the loan = 7 years
Interest rate = 6.75% compounded annually
2. Let's find the future value of this loan after 7 years, using the following formula:
FV = PV * (1 + r) ⁿ
PV = Loan = US$ 41,000
number of periods (n) = 7 (7 years compounded annually)
rate (r) = 6.75% = 0.0675
Replacing with the real values, we have:
FV = 41,000 * (1 + 0.0675) ⁷
FV = 41,000 * (1.0675) ⁷
FV = 41,000 * 1.5797
FV = US$ 64,767.70
We must pay back US$ 64,767.70 for the loan after 7 years.
WORTH 8 POINTS
What is the area of a rectangle with side lengths of 6/8 meter and 4/ 10 meter?
Answer:
3/10 (see picture for work)
Correction:I meant to write down [tex]a=l*h[/tex], not [tex]a=b*w[/tex].The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is calculated by multiplying the lengths together after simplifying them to 3/4 and 2/5, respectively. The resulting area is 0.3 m².
Explanation:To calculate the area of a rectangle, you multiply the length by the width. The question provides the side lengths as 6/8 meter and 4/10 meter. First, you may want to simplify these fractions to make multiplication easier. The fraction 6/8 simplifies to 3/4 after dividing both the numerator and the denominator by 2. The fraction 4/10 simplifies to 2/5 after dividing both the numerator and the denominator by 2.
Now, you multiply the simplified side lengths together to get the area:
Area = length × width
Area = (3/4) m × (2/5) m
Area = (3 × 2) / (4 × 5) [tex]m^2[/tex]
Area = 6 / 20 [tex]m^2[/tex]
Area = 3 / 10 [tex]m^2[/tex]
Area = 0.3 [tex]m^2[/tex]
The area of the rectangle is 0.3 [tex]m^2[/tex] (square meters).
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Find the length of the third side of each triangle
Answer:Where is the picture?
Step-by-step explanation:
What is 86 as a fraction in simplest form
Ron walked 3 3/4 km on monday,4 1/3 km on Wednesday. What distance did he walk in all
Answer:
Ron walked a total of 8 1/12 km
Step-by-step explanation:
Answer:
[tex]8\frac{1}{12} \; km[/tex]
Step-by-step explanation:
Distance walked by Ron on Monday = [tex]3\frac{3}{4} \; km[/tex]
Distance walked by Ron on Wednesday = [tex]4\frac{1}{3} \; km[/tex]
Now we will convert the given mixed fractions into improper fractions.
As we know that, a mixed fraction is composed of a whole number and a proper fraction.
Now,.
[tex]3\frac{3}{4} =\frac{3\times4+3}{4}=\frac{15}{4}[/tex]
[tex]4\frac{1}{3} =\frac{4\times3+1}{3} =\frac{13}{3}[/tex]
So, distance walked by Ron on Monday = [tex]\frac{15}{4}\; km[/tex]
Distance walked by Ron on Wednesday = [tex]\frac{13}{3} \; km[/tex]
Now, to find the total distance walked by Ron, we will add the distances walked by him on Monday and Wednesday.
So,
[tex]3\frac{3}{4} +4\frac{1}{3} =\frac{15}{4}+ \frac{13}{3}[/tex]
Now, we will find the LCM of the denominators of the given fractions.
The prime factorisation of 4 and 3 is,
4 = 2 × 2
3 = 3
So, LCM (3, 4) = 2 × 2 × 3 = 12
Now, we will convert each of the given fractions into their equivalent fractions with denominator 12.
[tex]\frac{15}{4}=\frac{15\times3}{4\times3}=\frac{45}{12}[/tex]
[tex]\frac{13}{3}=\frac{13\times4}{3\times4}=\frac{52}{12}[/tex]
So,
[tex]\frac{15}{4}+\frac{13}{3}=\frac{45}{12} +\frac{52}{12}=\frac{45+52}{12}=\frac{97}{12}[/tex]
Now, we will convert [tex]\frac{97}{12}[/tex] into improper fraction.
Now, 97 = 96 + 1 = 12 × 8 + 1
So, when '97' is divided by '12', then we get '8' as the quotient and '1' as the remainder.
So,
[tex]\frac{97}{12} = 8\frac{1}{12}[/tex]
Hence, Ron walked a total distance of [tex]8\frac{1}{12}[/tex] km in both the days.
Complete the inequality.
6 gal ___ 24 qt
Answer:
equal to.
Step-by-step explanation:
1 gallon would equal 4 quarts, So if 6 gallons were presnt multiply 6 and 4 and you get 24 quarts
The quantity in the inequality is the same for both sides, so you would use the equals sign. According to unit conversion, 6 gallons is equal to 24 quarts.
Explanation:The inequality you are trying to solve involves comparing the two quantities in gallons and quarts. One gallon is equivalent to 4 quarts. Therefore, we can multiply 6 gallons by 4 to convert it to quarts:
6 gal * 4 qt/gal = 24 qt
Therefore, the inequality would be: 6 gal = 24 qt
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A pipe that is 12 - feet long is cut into pieces that are 2 feet long. Which step below would give the
number of pieces into which the pipe is cut?
Answer:
Step-by-step explanation:
Number of pieces= total length/ length of one piece
= 12/2 = 6 pieces
Calculate the median of: 4.6, 3, 8.1, 9, 12,3, 9, 3.5, 7.3.
A. 5.8
B. 9
C. 3
D. 6.22
Answer: 7.3
Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.
Least to greatest ⇒ 3, 3, 3.5, 4.6, 7.3, 8.1, 9, 9, 12
So the median will be the middle number or 7.3.
Answer:
5.8
Step-by-step explanation:
First put all the numbers in order from least to greatest.
3, 3, 3, 3.5, 4.6, 7, 8.1, 9, 9, 12
There are two middle numbers, 4.6 and 7. Average them to get 5.8.
Solve the triangle. B = 73°, b = 15, c = 10
Incomplete Question, the complete question is
Solve the triangle.
B = 73°, b = 15, c = 10
A. C = 39.6°, A = 67.4°, a ≈ 14.5
B. Cannot be solved
C. C = 44.8°, A = 62.4°, a ≈ 14.5
D. C = 39.6°, A = 67.4°, a ≈ 20.3
Answer:
The Answer is the option A
A. C = 39.6°, A = 67.4°, a ≈ 14.5
Step-by-step explanation:
Given:
In Δ ABC,
∠B = 73°
b = 15
c = 10
To Find:
∠A = ?
∠B = ?
a = ?
Solution:
IN Δ ABC, Sine Rule says that
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
Substituting the given values we get
[tex]\dfrac{15}{\sin 73}= \dfrac{10}{\sin C}\\\\\sin C=0.6375\\\therefore C=39.6\°[/tex]
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\73+39.6+\angle A=180\\\therefore m\angle A =180-112.6=67.4\°[/tex]
∴ [tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}[/tex]
Substituting the given values we get
∴ [tex]\dfrac{a}{\sin 67.4}= \dfrac{15}{\sin 73}\\\\\therefore a=14.48\approx14.5[/tex]
Therefore,
A. ∠C = 39.6°, ∠A = 67.4°, a ≈ 14.5
solve the inequality 4y+3>2y+14
Step-by-step explanation:
Step 1. subtract 2Y from both sides
4y+3-2y>+14-2y 2y+3>14
step 2. subtract 3 from both sides
2y+3-3>14-3 2y>11
step 3. divide both sides by 2
2÷2y>11÷2 y>11÷2
answer is: y>11/ 2
The given inequality (4y + 3 > 2y + 14) is reduced to y > 5.5 and this can be evaluated by using the arithmetic operations.
Given :
Inequality -- 4y + 3 > 2y + 14
The following steps can be used to evaluate the given inequality:
Step 1 - Write the given inequality.
4y + 3 > 2y + 14
Step 2 - Subtract 3 from both sides in the above inequality.
4y + 3 - 3 > 2y + 14 - 3
4y > 2y + 11
Step 3 - Subtract 2y from both sides in the above inequality.
4y - 2y > 2y + 11 - 2y
Step 4 - Simplify the above inequality.
2y > 11
Step 5 - Divide by 2 on both sides in the above inequality.
y > 5.5
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