Amy runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?
A rectangular floor is 5 yards long and 4 yards wide. What is the area of the floor in square feet?
Final answer:
To calculate the area of the floor in square feet, the dimensions in yards are first converted to feet (1 yard = 3 feet), and then the length and width in feet are multiplied to get the area (15 feet x 12 feet = 180 square feet).
Explanation:
The student is asking about the area of a rectangular floor in square feet when the dimensions given are in yards. To find the area of the floor, we first convert the measures from yards to feet, knowing that 1 yard equals 3 feet. Therefore, the rectangular floor measures 5 yards long (which is 5 x 3 = 15 feet long) and 4 yards wide (which is 4 x 3 = 12 feet wide).
Now we can calculate the area by multiplying the length by the width. The area in square feet is thus 15 feet x 12 feet = 180 square feet.
Identify the slope and y-intercept of the graph of the equation. y = 1/4x + 3
A slope: 1/4 ; y-intercept: 3
B slope: 1/4; y-intercept: –3
C slope: 4; y-intercept: 3
D slope: 4 ; y-intercept: –3
Final answer:
The slope of the equation y = 1/4x + 3 is 1/4 and the y-intercept is 3, corresponding to option A: slope: 1/4 ; y-intercept: 3.
Explanation:
To identify the slope and y-intercept of the equation y = 1/4x + 3, we can compare it to the general form of the slope-intercept equation for a line, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept of the line. Thus, looking at the given equation, the coefficient of x (which is 1/4) is the slope, and the constant term (which is 3) is the y-intercept.
The correct answer is:
Slope: 1/4Y-intercept: 3Therefore, the answer is option A: slope: 1/4 ; y-intercept: 3
Paula completely covered a square wall using 87.5 ft2. Which is the side length of the wall?
Alisa hopes to play beach volleyball in the olympics someday. She has convinced her parents to allow her to set up a beach volleyball court in their backyard. A standard volleyball court is 26 feet by 52 feet. She figures she will need the sand to be one foot deep.
Sand a is 60 lbs for $5
Sand b is 150 lbs for $12
A. What's is the rate brand a is selling for? Give rate and then specify the unit rate.
B.Which brand is offering the better value? Explain.
Brand A is selling the sand at a rate of $0.0833 per pound, which is a slightly better value compared to brand B's rate of $0.08 per pound.
Explanation:A. To find the rate at which brand A is selling the sand, we need to calculate the cost per pound. The rate for brand A is $5 for 60 lbs. To find the unit rate, we divide the cost by the amount, which gives us $5 / 60 lbs = $0.0833 per lb.
B. To determine which brand is offering the better value, we compare the unit rates. Brand A has a unit rate of $0.0833 per lb, while brand B has a unit rate of $12 / 150 lbs = $0.08 per lb.
Therefore, brand A is offering a slightly better value since it has a lower unit rate.
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solve for g: 4gh+3=-8
Final answer:
To solve for g in the equation 4gh+3=-8 with H=-1, we substitute H and solve for g, resulting in g=11/4.
Explanation:
The question asks to solve for g in the equation 4gh + 3 = -8. To do this, we need to isolate g on one side of the equation. Given that H = -1, we can substitute this value into the equation, which simplifies to 4g(-1) + 3 = -8. This further simplifies to -4g + 3 = -8. Solving for g, we subtract 3 from both sides to get -4g = -11, and then divide both sides by -4 to get g = 11/4. Therefore, the solution is g = 11/4.
Write v as a linear combination of u and w, if possible, where u = (2, 2) and
w = (2, −3).
(Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.)
v = (4, −1)
The vector v = (4, -1) can be written as a linear combination of the vectors u = (2, 2) and w = (2, -3). The coefficients are both 1, which means that v = u + w.
Explanation:In this problem, we are trying to express the vector v = (4, -1) as a linear combination of the vectors u = (2, 2) and w = (2, -3). A linear combination means that we want to find coefficients a and b such that a*u + b*w = v.
Setting that equation up, we have:
a(2, 2) + b(2, -3) = (4, -1).
This leads to two equations:
2a + 2b = 4 and 2a - 3b = -1.
After solving this system of equations, we find that a = 1 and b = 1. Therefore, the vector v can be written as a linear combination of u and w as v = u + w.
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V can be written as v=u+w.
To express v as a linear combination of u and w, we need to find scalars a and b such that:
v = a * u + b * w
Given: u = (2, 2), w = (2, -3), and v = (4, -1)
We can set up the following system of equations based on the components:
2a + 2b = 4 (Equation 1 from x-components)
2a - 3b = -1 (Equation 2 from y-components)
Solving Equation 1 for 'a':
2a + 2b = 4
a + b = 2
a = 2 - b
Substituting 'a' in Equation 2:
2(2 - b) - 3b = -1
4 - 2b - 3b = -1
4 - 5b = -1
-5b = -5
b = 1
Substituting 'b' back into a = 2 - b:
a = 2 - 1
a = 1
Thus, v can be written as:
v = 1 * u + 1 * w
So, v = u + w
estimate the answer to: 3772 divided by 44
The container that holds the water for the football team is 1/3 full. After pouring out 6 gallons of water it is 1/9 full. How many gallons can the container hold?
The container cannot hold a specific number of gallons.
Explanation:To solve this problem, we can use a proportion. Let's assume that the number of gallons the container can hold is According to the problem, the container is initially 1/3 full, so we can write this as 1/3 of After pouring out 6 gallons of water, it becomes 1/9 full, which we can write as 1/9 of Setting up the proportion, we have:
1/3 of = 1/9 of
To solve for we can cross multiply:
9 * (1/3) * = 1 * (1/9) *
Canceling out the variables and multiplying, we have:
3= /9
Multiplying both sides by 9, we get:
27=
Dividing both sides by , we have:
27 = 1
Since the equation is not true, we have a contradiction. This means there is no solution, or the container cannot hold a specific number of gallons.
Final answer:
The total capacity of the football team's water container is 27 gallons. We determine this by comparing the change in water level from being 1/3 full to 1/9 full after removing 6 gallons and calculating proportionally.
Explanation:
To solve the problem regarding the water container for the football team, we need to find out the total capacity of the container. When 6 gallons of water is poured out, it results in the container being 1/9 full rather than 1/3, which means the removal of 6 gallons of water equates to 1/3 - 1/9 of the container's capacity.
First, let's find the common denominator for 1/3 and 1/9 which is 9. So the difference in the water level when the 6 gallons were removed is (3/9 - 1/9) or 2/9 of the container's capacity. This tells us that 2/9 of the container's capacity is equal to 6 gallons.
Step-by-Step Calculation
Set up the proportion: 2/9 = 6 gallons.
To find the full capacity, we solve for 9/9 (which is the whole): (9/9) / (2/9) = X / 6 gallons.
Cross multiply to solve for X: 2X = 54.
Divide both sides by 2: X = 27.
Therefore, the total capacity of the water container is 27 gallons.
Use counters to find the quotient and remainder for 36 divide a by 8
A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.
Which of the following are valid names for the given triangle below? Check all that apply.
Answer:
Triangle LMZ
Triangle MLZ
Triangle ZML
Step-by-step explanation:
Option A,B and E are all the valid names.
The valid names of the triangle are those that has all the angles withing. The angles are Angle l, M and Z.
C and D are not angles, so any triangle cannot be formed using these.
Hence, the valid triangles here are:
Triangle LMZ
Triangle MLZ
Triangle ZML
Answer:
LMZ,ZML,MLZ
Step-by-step explanation:
Let k(t) be a measure of the knowledge you gain by studying for a test for t hours. which do you think is larger, k(8) − k(7) or k(3) − k(2)
To determine which is larger between k(8) - k(7) and k(3) - k(2) , compare the specific values. If the graph of k(t) is concave upward, studying more hours yields a larger knowledge increase.
To determine which is larger between k(8) - k(7) and k(3) - k(2) , and to understand the concavity of the graph of k(t) , consider the following:
1. Larger Increase in Knowledge:
- Evaluate k(8) - k(7) and k(3) - k(2) .
- If k(8) - k(7) is greater, it implies that studying for an additional hour (from 7 to 8 hours) provides a larger increase in knowledge than studying for an hour from 2 to 3 hours.
2. Concavity of the Graph:
- If k''(t) > 0 (second derivative is positive), the graph is concave upward.
- If k''(t) < 0 (second derivative is negative), the graph is concave downward.
3. Reasoning for Concavity:
- If the graph is concave upward, it suggests that the rate of knowledge gain is increasing. Studying more hours leads to a larger increase in knowledge.
4. Final Answer:
- The comparison between k(8) - k(7) and k(3) - k(2) depends on the specific function k(t) . As for concavity, if the graph is concave upward, studying more hours yields a larger increase in knowledge.
In summary, compare the specific values k(8) - k(7) and k(3) - k(2) and analyze the concavity of the graph to determine the relationship between studying hours and knowledge gain.
Question. Let k(t) be a measure of the knowledge you gain by studying for a test for t hours, . Which do u think is larger, k(8)-k(7) or k(3) - k(2) ? is the graph of k concave upward or concave downward? why?
In the diagram, what is the value of x
The sum of angles on a straight line is 180degrees. The measure of the value of x from the figure is 98degrees
Sum of angle on a straight lineThe measure of angles 82 degrees and the unknown are on a straight line, Since the sum of angles on a straight line is 180degrees, hence;
x + 82 = 180
Subtract 82 from both sides
x + 82 - 82 = 180 - 82
x = 180 - 82
x = 98 degres
Hence the measure of the value of x from the figure is 98degrees
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How many ways can a person with five nickels, three dimes, and two quarters make a 75-cent purchase from the machine?
What is the value of 4 in the number 358.547? please help!!!!!
A) 0.0004
B) 0.004
C) 0.04
D) 4
Which choice solves the problem?
1467÷7=
A) 27
B) 29 with a remainder of 4
C) 207 with a remainder of 4
D) 209 with a remainder of 4
Bailey’s horse is growing fast. She ate 2 scoops of feed in the morning, 4 scoops in the afternoon and 3 scoops at night. She did this all week long. How many scoops of feed did Bailey’s horse eat over the course of the week?
A) 2 x 3 x 4
B) 2 x (3 + 4)
C) 2 + 3 + 4 + 7
D) (2 + 3 + 4) x 7
Katie earned $1200 in 8 years on an investment at a 6% annual simple interest rate. How much was Katie’s investment?
$945
$2500
$4500
$9000
Miranda buys 6 pounds of nuts. if she puts 3/4 pound in each bag, how many bags can she make?
Answer:
Number of bags Miranda makes equals:
8
Step-by-step explanation:
Miranda buys 6 pounds of nuts.
She puts 3/4 pound in each bag
Let she makes x bags
then total nuts in x bags=[tex]\dfrac{3}{4}x[/tex]
also total nuts must be equal to 6
i.e. [tex]\dfrac{3}{4}x=6[/tex]
Multiplying both sides by 4, we get
3x=24
Dividing both sides by 3, we get
x=8
Hence, number of bags Miranda makes equals:
8
Planet Strusenope travels one full rotation around its sun in approximately 365.25 days. How many minutes does it take for Strusenope to travel one full rotation around the sun?
56 books 75% decrease
When using a multiplicative power function (y = a x1b1 x2b2 x3b3) to represent an economic relationship, estimates of the parameters (a, and the b's) using linear regression analysis can be obtained by first applying a ____ transformation to convert the function to a linear relationship?
Alex has 48 stickers. This is 6 times the number of stickers max has. How many many stickers does max have?
What is the slope, m, and the y-intercept of the line that is graphed below?
Answer: The correct option is
(A) m = 1; (0, 3).
Step-by-step explanation: We are given to find the slope, m, and the y-intercept of the graphed line.
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the graph, we note that the line passes through the points (-3, 0) and (-1, 2).
Therefore, the slope of the graphed line will be
[tex]m=\dfrac{2-0}{-1-(3)}=\dfrac{2}{2}=1.[/tex]
Also, at x = 0, the value of the y-coordinate is 3. So, the y-intercept of the line is (0, 3).
Thus, the slope, m = 1 and the y-intercept is (0, 3).
Option (A) is CORRECT.
According to modern science, Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose the entire history of Earth is represented with a 100-meter-long timeline, with the birth of Earth on one end and today at the other end. a. What distance represents 11 billion years? b. How far from the end of the timeline does written human history begin?
Answer:
A- The distance that represents 11 billion years is 244.4 meters.
B- Written human history begins 0.2 milimeters far from the end of the timeline.
Step-by-step explanation:
A- We can solve this problem by using crossed multiplication.
4,5 billion years --- 100 meters
11 billion years --- X
11 x 100 / 4,5 = X
X= 244.4
B- Once again, this can be solved using crossed multiplication.
If 4,500,000,000 years are represented in 100 meters, that would be:
4,500,000,000 --- 100 meters
10,000 --- X
10,000 x 100 / 4,500,000,000 = X
X= 0.0002 meters
0.0002 meters are 0.2 milimeters
In circle Y, what is m∠SZT? 86° 94° 108° 128°
Answer:
It's 94
Step-by-step explanation:
Find the quotient 5/18 divided by 2/6
To divide fractions, multiply the first fraction by the reciprocal of the second fraction and simplify if possible.
Explanation:To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is found by switching the numerator and denominator. So, to divide 5/18 by 2/6, we will multiply 5/18 by 6/2.
First, we cancel out any common factors between the numerators and denominators:
5/18 * 6/2 = (5 * 6)/(18 * 2) = 30/36.
Now, we can simplify 30/36 by finding the greatest common divisor (GCD) of 30 and 36, which is 6.
Dividing both the numerator and denominator of 30/36 by 6, we get the final quotient of 5/6.
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When the consumer price index decreases from 200 to 150, prices decrease by 50%.
A. True
B. False
Answer:
Apex answer: FALSE
Step-by-step explanation:
Final answer:
The consumer price index decreasing from 200 to 150 represents a 25% decrease, not 50% as incorrectly stated.
Explanation:
The statement that prices decrease by 50% when the consumer price index (CPI) decreases from 200 to 150 is false. To calculate the percentage decrease in CPI, we use the formula for percentage change: ((new value - original value) / original value) × 100. In this case, ((150 - 200) / 200) × 100 = (-50 / 200) × 100 = -25%. This shows that there is a 25% decrease in the CPI, not 50%.
The correct calculation reveals that the decrease in the Consumer Price Index (CPI) is 25%, not 50%.
Understanding the accurate interpretation of percentage changes is crucial for assessing economic indicators and making informed decisions.
Banks and other financial institutions sometimes calculate simple interest based on
What is the slope of a line that is parallel to the line shown on the graph?
A.–3
B.-1/3
C.1/3
D. 3
The slope of a line that is parallel to the line shown on the graph is -3.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The slope of a line from its graph by looking at the rise and run.
The vertical change between two points is called the rise, and the horizontal change is called the run.
One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.
Now take points (0,2) and (1,-1)
[tex]Slope = \frac{rise}{run}[/tex]
Line slants down from left to right. So line has a negative slope.
⇒ [tex]Slope =\frac{y2-y1}{x2-x1}[/tex]
⇒ [tex]Slope =\frac{-1-2}{1-0}[/tex]
⇒ [tex]Slope = -3[/tex]
The slope of the line that is parallel to the given line is same as that of the line.
Hence we can conclude that the slope of a line that is parallel to the line shown on the graph is -3.
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What is cultural imperialism?
the impact of a nation’s culture on its trade policies
the imposition of a foreign culture on a nation’s population
the impact of culture on people’s buying and spending habits
the spread of foreign culture through immigrants from various nations
Answer:
The correct answer is : B) the imposition of a foreign culture on a nation's population.
Step-by-step explanation:
Cultural imperialism shows the cultural aspects of imperialism that is a culture being imposed on other countries.
And imperialism can be defined as maintaining the unequal relationships between civilizations.
So, the correct answer is : B) the imposition of a foreign culture on a nation's population.