Which number line shows the solution to −6 − (−4)? A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 10 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to 6 is shown. Above this, another arrow pointing from 6 to 10 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow. A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to 6 is shown. Above this, another arrow pointing from 6 to 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

The largest rectangular orchid garden that can be enclosed within a $120 budget, considering the given costs of fencing, has dimensions of 2 feet by 2 feet, resulting in an area of 4 square feet.

You wish to create a rectangular orchid garden with the house forming the northern boundary, and you're working with a budget of $120 for fencing. The cost per foot for the southern boundary is $30, and for the east and west sides, it's $15 each. We need to determine the dimensions that maximize the area.

Let's denote the width of the garden (east and west sides) as w feet, and the length (only the southern side, as the northern side is the house) as l feet. The total cost of fencing is therefore the sum of the costs for all three sides: Cost = $30l + 2($15w), which simplifies to Cost = $30l + $30w. Since your budget is $120, we can write the equation $30l + $30w = $120, which simplifies further to l + w = 4.

To find the dimensions that give you the largest area, we need to maximize the area A of the rectangle, which is A = l  imes w. Substituting w with 4 - l (from our previous equation), we get A = l  imes (4 - l). To find the maximum area, take the derivative of A with respect to l and set it to zero, solving for l. This gives us l = 2 feet. Substituting back, we find w = 2 feet as well.

The dimensions for the garden that will give you the largest enclosed area within a $120 budget are 2 feet in width by 2 feet in length, resulting in an area of 4 square feet.

Answer:

Option (a) is correct.

The value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55

Step-by-step explanation:

  Given : [tex]f(x) = -2x^2 + 4x- 7[/tex]

We have to find the value at f(-4) and choose the correct option from the given options.

Consider the given function [tex]f(x) = -2x^2 + 4x- 7[/tex]

Since, we have to find the value of f(-4) that is value of f(x) at x = -4

Substitute, value of x = -4 in given function, we have,

[tex]f(-4) = -2(-4)^2 + 4(-4)- 7[/tex]

Simplify, we have,

[tex]f(-4) = -55[/tex]

Thus, the value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55

Option (a) is correct.

The velocity of the bus is:

velocity (bus) = 36 miles / 40 min

velocity (bus) = 0.9 miles / min

Since the car is 1.5 times faster, so the velocity of the car is:

velocity (car) = 1.5 * 0.9 miles / min

velocity (car) = 1.35 miles / min

At the meeting point, the sum of the distance is equal to 36 miles. Therefore:

1.35 t + 0.9 t = 36

2.25 t = 36

t = 16 min

So they will meet after 16 minutes.

The question pertains to a basic subtraction operation where the student is left with 7 boxes of carrots after subtracting 68 boxes from an initial count of 75 boxes.

The subject of the question is mathematics, specifically involving subtraction and the concept of determining the number of items remaining after a reduction. The mathematical operation presented in the question is 75 boxes - 68 boxes = 7 boxes, which indicates that when you start with 75 boxes of carrots and remove 68 boxes, you are left with 7 boxes of carrots.

This type of problem is common in elementary mathematics and does not involve complex concepts such as permutations, probability, or statistical distributions.

Harvey earned a simple interest of $660 over 2 years on his $6000 investment.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, We know that;

Simple interest is calculated using the formula:

I = P r t

Where: I = Interest earned P = Principal amount (amount invested) r = Annual interest rate t = Time period (in years)

Now, In this case,

Harvey invested $6000 for 2 years at an annual interest rate of 5.5%.

So, using the formula:

I = 6000 x 0.055 x 2

I = $660

Therefore, Harvey earned a simple interest of $660 over 2 years on his $6000 investment.

Learn more about the multiplication visit:

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Ok so if she needs 64 floz, If u add 5+3 you get 8. 64/8 = 8

Now You multiply your parts of water and juice by 8.      

5*8= 40   <---- Answer

3*8 =24  <----Answer

To check your answer you would add up the parts of each. 40+24= 64

Answer: Yes , Rajendra has enough trail mix  to completely fill 8 bags.

Step-by-step explanation:

Given : Total trail mix Rajendra has = [tex]14\dfrac{4}{5}[/tex] pounds

Convert [tex]14\dfrac{4}{5}[/tex]  into improper fraction.

[tex]14\dfrac{4}{5}=\dfrac{(14)(5)+4}{5}=\dfrac{74}{5}[/tex]

Amount of mix in each bag = [tex]1\dfrac{1}{2}[/tex] pounds.

[tex]=\dfrac{1(2)+1}{2}=\dfrac{3}{2}[/tex] pounds

Then, the total number of bags can be filled by the trail mix Rajendra has

= Total trail mix ÷ Amount of mix in each bag

[tex]=\dfrac{74}{5}\div\dfrac{3}{2}[/tex]

[tex]=\dfrac{74}{5}\times\dfrac{2}{3}=\dfrac{148}{15}=9.86666666667\approx9[/tex]

It means Rajendra has enough trail mix to fill 9 bags.

Since 9 > 8

Therefore , Rajendra has enough trail mix  to completely fill 8 bags.

Answer:

C. Use the straightedge to draw XR←→ and XS←→.

Step-by-step explanation:

Adam has drawn the arcs by using RS distance as the radius of the circle and mid points as R and S.

So the point X is the same distance from R and S.

So now Adam has to use the straightedge to draw XR←→ and XS←→.

Then,  XR = XS = RS

So it is an equilateral triangle.

Therefore, the correct answer is C.

Adam should do for his next step to use the straightedge to draw [tex]\( XR \)[/tex] and [tex]\( XS \).[/tex] The option (C) is correct.

The construction process for the equilateral triangle:

To construct an equilateral triangle using a straightedge and compass:

Construct [tex]\( XR \)[/tex]: Adam has already constructed segment [tex]\( XR \).[/tex]

Draw [tex]\( XS \)[/tex]: Using the straightedge, Adam should draw a line segment [tex]\( XS \)[/tex] from point [tex]\( X \)[/tex] to another point [tex]\( S \)[/tex] such that [tex]\( XS = XR \)[/tex]. This ensures that two sides of the equilateral triangle are equal in length.

Draw [tex]\( RS \)[/tex]: After drawing [tex]\( XS \)[/tex], Adam should use the straightedge to draw segment [tex]\( RS \)[/tex], completing the equilateral triangle [tex]\( \triangle XRS \).[/tex]

This method aligns with the steps typically used in geometric constructions to form an equilateral triangle: ensuring that all three sides are equal in length by first establishing two sides of equal length and then completing the triangle.

Therefore, upon reconsideration, option (C) is indeed the correct next step for Adam to construct his equilateral triangle.

Answer:

Total number of cards in shuffled deck=3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6, 4 , 5 , K , 2 , 7 , 6 , A , J , J , A .

Total number of cards in a deck of card = 52 cards, out of which 26 are black cards and 26 are red card.

As, it is not given that out of the 20 cards dealt by dealer is either red card or black card.

A=3=2B +1 R or 1 B + 2 R

2=4=2 R +2 B

3=1=1 R or 1 B

4=1=1R or 1 B

5=2=2 R or 2 B

6=2=2 R or 2 B

7=1=1 R or 1 B

8=0

9=0

10=0

J=2= 2 R or 2 B

K=3= 2 R + 1 B or 1 R +2 B

Q=1=1 R or 1 B

If you count total number of black cards among the number of cards dealt by dealer, the possibilities of black card drawn is either 15 or 16 from 20 cards drawn.

As, Experimental probability is the probability obtained through experiment which is different from theoretical Probability.

Total number of cards =52

So, Probability of dealing with black cards by dealer which is either 15 or 16 in number is given by

[tex]=\frac{\text{total favorable outcome}}{\text{total possible outcome}}\\\\\frac{15}{52} {\text{or}} \frac{16}{52}=\frac{4}{13}.[/tex]

40%

There are 20 cards in total.

8 are black: 3,2,K,5,6,4,A,J

12 are red: 2,A,K,Q,2,5,K,2,7,6,J,A

so that means 8 of the 20 are black or 8/20

and 8/20 is 40% which is your answer.

y = (slope)x + (y-intercept)

y = -1/2x - 2

x-intercepts occur when y = 0

0 = -1/2x - 2

2 = -1/2x

x  = -4

Thus, the x-intercept is at (-4,0)

Answer:

Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

Step-by-step explanation:

It is called the inverse or reciprocal function of f to another function f − 1 that fulfills that:

If f (a) = b, then f − 1 (b) = a.

The inverse of a function when it exists is unique, so that neither "X" nor "Y" can be repeated.

If we analyze the possibilities, in the case of b, c, and d, the value 4 of the "Y" is repeated twice; in the case of a, that does not happen, therefore the answer is: a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2) }

Answer:

[tex]\frac{1}{16}[/tex]

Step-by-step explanation:

We are given that

Trygg has package of marigold seeds=[tex]\frac{3}{4}[/tex]

He plants  seeds in garden=[tex]\frac{1}{6}\times \frac{3}{4}=\frac{1}{8}[/tex]

Remaining seeds=[tex]\frac{3}{4}-\frac{1}{8}=\frac{5}{8}[/tex]

He divide remaining seeds equally into 10 flower pots.

We have to determine the fraction of a package of seeds is planted in each flower pot.

Seeds in each pot=[tex]\frac{\frac{5}{8}}{10}=\frac{1}{16}[/tex]

Hence, seeds planted in each pot=[tex]\frac{1}{16}[/tex]

Final answer:

The space between two objects is measured as distance or length, with miles being the correct unit of measurement among the given options.

Explanation:

The measurement of the space between two objects is referred to as length or distance. If we look at the options provided: A. Area, B. Pounds, C. Circumference, D. Miles, it is clear that miles is a unit of measurement that describes distance. Area measures the size of a surface, pounds measure weight or mass, and circumference measures the distance around a circle. When considering distances, especially those that are long such as between two cities, miles is an appropriate unit to use. For example, the distance between your house and school would best be measured in kilometers or miles, rather than in smaller units like inches or centimeters, or in unrelated units like pounds or areas.

Final answer:

The distribution of sample means for college presidents' incomes, based on many different samples of size 40, will approximate a normal distribution due to the Central Limit Theorem.

Explanation:

The question regarding the distribution of sample means for college presidents' incomes pertains to a concept in statistics known as the Central Limit Theorem. When dealing with a population whose distribution is skewed, the distribution of sample means tends to become approximately normal if the sample size is large enough, which is usually considered to be over 30. As multiple samples of size 40 are taken in this case, the distribution of the sample means for the college presidents' annual incomes should approximate a normal distribution.

Explaining the calculation of the amount in the account after 3 years and the compound interest earned.

Amount in the account after 3 years:

Calculate the monthly interest rate: 6.5% annual interest divided by 12 (months) = 0.0054167

Calculate the total amount using the compound interest formula: $12,500 * (1 + 0.0054167)^36 = $15,183.41

Compound interest earned:

Subtract the initial deposit from the total amount: $15,183.41 - $12,500 = $2,683.41

Let us say that:

x = weight of llamas

y = weight of okapi

From the problem, we can create the equations:

x + y = 450           --> 1

3 x = y + 190        --> 2

Rewriting equation 1:

x = 450 – y

From equation 2:

3 (450 – y) = y + 190

1350 – 3 y = y + 190

4 y = 1160

y = 290

From equation 1:

x = 450 – 290

x = 160

Therefore a llama weighs 160 kilograms while okapi weigh 290 kilograms on average.