A salesperson had $240,000 in sales last year, which is 60% of the sales she had this year. Which equation could be used to determine x, the salesperson's total amount in sales, in dollars, for this year?

Answer:

The student made an error in step 3.

Step-by-step explanation:

Step 2 is correct but 42/-6 is 12.

Answer:

The correct answer is C. f(x) = x - 7

Step-by-step explanation:

In order to find this, you simply need to know that vertical shifts can be added on to the end of parent equations as constants. Since this is a downward shift, we use a negative number.

Answer:

Choice D which is 6x - 9(-4x + 8) = 12

Step-by-step explanation:

The first equation solves to y = -4x+8 when you subtract 4x from both sides. This to undo the addition of 4x done to y.

Then you replace every copy of "y" in the second equation with (-4x+8). The parenthesis is important so that you multiply properly

We go from 6x - 9y = 12 to 6x - 9( -4x+8 ) = 12

The resulting equation after an equivalent expression for y is substituted into the second equation is 6x - 9(-4x + 8) = 12, option D.

The student asks about substituting an expression for y from the first equation into the second equation in a system of linear equations. The first equation gives us y in terms of x, which can be expressed as y = 8 - 4x. Substituting this expression into the second equation, 6x - 9y = 12, will result in the compound equation 6x - 9(8 - 4x) = 12. which is same as 6x - 9(-4x + 8) = 12 , option D.

Answer:

The correct answer option is: [tex]\frac{1}{3} ,\frac{1}{4} ,\frac{1}{5} ,\frac{1}{6}[/tex].

Step-by-step explanation:

We know that the [tex]nth[/tex] term [tex]a_n[/tex] for an arithmetic sequence is given by:

[tex]a_n=\frac{(n+1)!}{(n+2)!}[/tex]

where [tex]n[/tex] is the number of the position of the term.

We are supposed to find the first four terms of the sequence so we will substitute the values of [tex]n[/tex] from 1 to 4 in the given formula to get:

1st term:

[tex]a_1=\frac{(1+1)!}{(1+2)!}=\frac{1}{3}[/tex]

2nd term:

[tex]a_2=\frac{(2+1)!}{(2+2)!}=\frac{1}{4}[/tex]

3rd term:

[tex]a_3=\frac{(3+1)!}{(3+2)!}=\frac{1}{5}[/tex]

4th term:

[tex]a_4=\frac{(4+1)!}{(4+2)!}=\frac{1}{6}[/tex]

This problem is solved by using the concept of percentage as a part of a whole. We find out that 30% of the total distance equals 6 miles. So by setting up the proportion 30/100 = 6/x, we calculate the total distance is 20 miles.

This question is an application of percentage problems in real-life situations, specifically hiking distance. When you use a percentage to describe a part of a whole thing, the thing is always considered to be '100%'. In this case, Michelle's hiking trip is the 'whole thing' or '100%'.

We are told that 6 miles is 30% of the total distance. To find the total distance, we can set up a proportion to solve for it. The proportion would be 30/100 = 6/x.

Let x represent the total distance. So we can write the proportion as:

6 / x = 30 / 100

To solve for x, we can cross multiply and then divide:

100 * 6 = 30 * x

600 = 30x

x = 20

Therefore, the total number of miles Michelle will walk is 20 miles.. So, the total distance that Michelle will walk is 20 miles.

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Answer:

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\triangle RST=\triangle NPQ[/tex]

[tex]m\angle R=-7x+9,m\angle N=-10x[/tex]

We have to find the measure of angle R and measure of angle N.

When two triangles are equal then their angles are equal

Therefore, [tex]m\angle R=m\angle N[/tex]

[tex]-7x+9=-10x[/tex]

[tex]-7x+10x=-9[/tex]

By subtraction property of equality

[tex]3x=-9[/tex]

By combine like terms

[tex]x=\frac{-9}{3}=-3[/tex]

By division property of equality

Substitute x=-3 then we get

[tex]m\angle R=-7(-3)+9=21+9=30^{\circ}[/tex]

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Answer:

30

Step-by-step explanation:

The required number of dinosaurs that each of them gets is 39 dinosaurs.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of dinosaurs be x that is distributed among Yolanda and her 3 brothers,
Total persons = 1 + 3 = 4
Total dinosaurs = 156
Each of them gets,
x = 156/4
x = 39 dinosaurs.

Thus, the required number of dinosaurs that each of them gets is 39  dinosaurs.

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Answer:

168 Km

Step-by-step explanation:

divide 132 Km by 11 to find distance travelled with 1 litre and then multiply this by 14 for distance travelled with 14 litres

= [tex]\frac{132}{11}[/tex] × 14 = 168 Km

Answer: (A) 19.3%

Step-by-step explanation:

[tex]\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15[/tex]

Vodka + Vermouth + Olive = Total Cost

$2.59  +   $0.12      + $0.15 = $2.86

[tex]\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%[/tex]

Answer:

f(n) = 10 * 5^(n-1)

an = 15-2.5n

Step-by-step explanation:

{(1, 10), (2, 50), (3, 250), (4, 1250)}

The formula for a geometric sequence is

an = a1 * r ^(n-1)

where a1 is the first term and r is the rate in which it increase

a1 =10

r = 5,  each term goes up by a factor of 5

50/10 = 5

250/50 = 5

etc

f(n) = 10 * 5^(n-1)

What is the explicit rule for the sequence?

13, 10.5, 8, 5.5, 3, 0.5, ...

For an arithmetic sequence the formula is

an = a1 + d(n-1)

where a1 is the first term and d is the common difference

a1= 13 and d = -2.5

10.5 -13 = -2.5

8. - 10 = -2.5

etc

an = 13 - 2.5 ( n-1)

Simplifying

an = 13 -2.5n + 2.5

an = 15-2.5n

Answer: 25.13 (choice B)

================================

The formula we'll use is

s = r*theta

with

s = unknown arc length

r = radius = diameter/2 = 12/2 = 6 feet

theta = 4pi/3 radians <--- this angle must be in radian mode for the formula to work

Plug those values into the formula and simplify

s = r*theta

s = 6*(4pi/3)

s = 24pi/3

s = 8*pi

s = 8*3.1416

s = 25.1328

s = 25.13

which is approximate and rounded to the nearest hundredth.

Option: B is the correct answer.

The range of the function is:

        B.      5 < y < ∞

Range of a function--

The range of a function is the set of all the values that is attained by the function.

By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞

Also, the function is a strictly increasing function.

This means that the function takes every real value between 5 and ∞ .

i.e. The range of the function is: (5,∞)

          Hence, the answer is:

                Option: B

Answer: 24.6 inches

Step-by-step explanation: Since it's a rectangle, and not a rectangular prism, that means it's 2D. Length is the long sides on the top and bottom, and width is the shorter sides on it's left and right. So since there's two of each, just do 8.1 + 8.1 + 4.2 + 4.2 and you have your answer!

Answer:

B  2,3,-3

Step-by-step explanation:

If we use the zero product property, we can set each term =0 to find the roots.

0=(x-2)(x-3)(x+3)

x-2 =0   x-3 =0   x+3=0

x=2   x=3          x=-3

The roots are -3,2,3

Answer:

decrease

Step-by-step explanation:

75 is a higher than 25% come man its ez

The value of y and x is 11 and 6.  

The m<BED = 40 degrees

The m<BEA = 40 degrees.

From the given diagram, the following statements are true:

AB = BC

3y = 5y - 22

3y - 5y = -22

-2y = -22

y = 11

Similarly, m<DBE = 50 degrees

m<BED = 90 - m<DBE

m<BED = 90 - 50

m<BED = 40 degrees

Since BE = BC = 3y

BE = BC = 3(11) = 33

Also, 7x  - 2 = 40

7x = 40 + 2

7x = 42

x = 6

Get the measure of m<BEA

m<BEA = 7x - 2

m<BEA = 7(6) - 2

m<BEA = 40 degrees

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Question

Describe how to find all the points on a baseball field that are equidistant from second base and third base.

In the figure, m∠DBE=50. Find each of the following.

m∠BEDm angle b e d

m∠BEAm angle b e eh

x

y

BE

BC

Answer: Choice A

S9 = (9/2)*(2+26)

===============================================

The formula is

Sn = (n/2)*(a1+an)

where

Sn = sum of the first n terms (nth partial sum)

n = number of terms

a1 = first term

an = nth term

In this case,

n = 9

a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)

an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)

So,

Sn = (n/2)*(a1+an)

S9 = (9/2)*(2+26)

will help us find the sum of the first 9 terms of this arithmetic sequence

Answer:

A. S9 = (9/2)*(2+26)

Answer:

Step-by-step explanation:

The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.

Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole

(100 - x) * tan(30) = x*tan(60)

The distance to the other pole = 100 - 25 = 75

[tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].

To simplify the expression [tex]\( -3 d^8(-4 d^{-14}) \)[/tex], you can follow these steps:

1. Distribute the factor [tex]\(-3\)[/tex] to both terms inside the parentheses.

2. Combine the exponents with the same base [tex](\(d\))[/tex].

Let's work through it step by step:

[tex]\[ -3 d^8(-4 d^{-14}) \][/tex]

1. Distribute [tex]\(-3\)[/tex] to both terms inside the parentheses:

[tex]\[ (-3) \cdot d^8 \cdot (-4) \cdot d^{-14} \][/tex]

[tex]\[ = 12 d^8 d^{-14} \][/tex]

2. Combine the exponents with the same base [tex](\(d\))[/tex] by applying the rule [tex]\(a^m \cdot a^n = a^{m+n}\)[/tex]:

[tex]\[ = 12 d^{8 + (-14)} \][/tex]

[tex]\[ = 12 d^{-6} \][/tex]

Therefore, [tex]\( -3 d^8(-4 d^{-14}) \)[/tex] simplifies to [tex]\(12 d^{-6}\)[/tex].

The complete question is given below:

Simplify [tex]\( -3 d^8(-4 d^{-14}) \)[/tex]. Assume that  [tex]d \neq 0[/tex].

the answer is 12/d^6 , D

The account with the greater principal is Account B with a simple interest of $ 18

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the first account be = A

Let the second account be = B

Now ,

The simple interest of A = $ 4.50

The simple interest of B = $ 18

The time period t = 18 months = 1.5 years

The rate of interest r for A = 2 %

The rate of interest r for B = 4 %

Now , the equation will be

Simple Interest of A = ( Principal of A x Rate of interest of A x Time ) / 100

Substituting the values in the equation , we get

4.50 = ( P x 2 x 1.5 ) / 100

Multiply by 100 on both sides of the equation , we get

450 = 3P

Divide by 3 on both sides of the equation , we get

Principal of A = $ 150

And ,

Simple Interest of B = ( Principal of B x Rate of interest of B x Time ) / 100

Substituting the values in the equation , we get

18.00 = ( P x 4 x 1.5 ) / 100

Multiply by 100 on both sides of the equation , we get

1800 = 6P

Divide by 6 on both sides of the equation , we get

Principal of B = $ 300

Therefore , the principal of B > principal of A

Hence , the simple interest of B with $ 18 has larger principal

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Answer:

[tex]y^2=-12(x+2)[/tex]

Step-by-step explanation:

The general vertex form of parabola is,

[tex](y-k)^2=a(x-h)[/tex]

where,

[tex](h.k)[/tex] is the vertex,

[tex]y=h[/tex] is the axis of symmetry.

Given the coordinates of the vertex as [tex](-2,0)[/tex] and focus as [tex](-5,0)[/tex]

a is the 4 times the distance between the vertex and the focus.

The distance between the vertex and focus is -3. Negative is because we are calculating the distance to the left (-ve x direction) of the vertex.

Hence, [tex]a=4\times(-3)=-12[/tex]

Putting the values in the general equation,

[tex](y-0)^2=-12(x-(-2))[/tex]

i.e [tex]y^2=-12(x+2)[/tex]

Answer:

The perpendicular line would be y = 6

Step-by-step explanation:

In order to get this, we must first recognize that the equation given is a vertical line. If our new line is to be perpendicular to it, it must be a horizontal line. All horizontal lines are written as y = (a number). Since we have a point it goes through, we can get that value in the ordered pair. The ordered pair has a y value of 6, which means the equation would be y = 6

Problem 1

Answers:

Percentage of patients that were dogs = 46%

Standard Error = 0.07048404074682

Margin of error for 90% confidence interval = 0.11594624702851

Margin of error for 95% confidence interval = 0.13814871986377

Round the decimal values however you need them

------------

To get the first answer, you add up the numbers given (7,4,5,5,2) and divide that over 50. So 7+4+5+5+2 = 23 which leads to 23/50 = 0.46 = 46%; therefore phat = 0.46 is the sample proportion of dogs.

Use the SE (standard error) formula given to you with phat = 0.46 and n = 50 to get SE = 0.07048404074682

The critical z value at 90% confidence is 1.645; this value is found in your Z table (back of your stats textbook). Multiply the SE value by 1.645 to get 0.07048404074682*1.645 = 0.11594624702851

Also found in your textbook is 1.960 which is the z critical value at 95% confidence. Multiply this with the SE value to get 0.07048404074682*1.960 = 0.13814871986377

===============================================

Problem 2

Answer: Choice B) picking balls from a bin; the 60 randomly selected get chosen for the first bus, while the remaining 60 go to the second bus

-----------

Choice A is fairly vague on what the lower and upper boundaries are. What is the smallest number allowed? What about the largest? This isn't clear so it's possible that we could end up with more positive numbers than negative (eg: if we had an interval -10 < x < 110). So choice A is false. A similar issue shows up with choice D.

Choice B is true. Assuming the selection process is random and not biased, then each ball is equally likely for each selection. The fact that the balls are colored seems to be extra info which I'm not sure why your teacher threw that in there.

Choice C is false because choice B is true

Choice D is false for similar reasons as choice A. It's not clear where we start and where we end. If we had the interval 2 < x < 6 then x could take on the values {3, 4, 5} and we see that picking an odd number is twice as likely than picking an even. In this example, there is bias.

===============================================

Problem 3

Answer: Choice B) Roll a die; each number corresponds to a different class

------------

Choice A is false because choice B being the answer contradicts it

Choice B is true: there are 6 sides on the die, and each side is equally likely to be landed on, so each class is equally likely

Choice C is false because 2*2*2 = 8 represents the number of combos you can have when you flip three coins (one combo being HTH for heads tail heads) but there are 6 classes, not 8

Choice D is false because while we want 6 regions on the spinner. Each region must have the same area; otherwise, one class is weighted heavier than the others making it more likely you select that particular class.

The guy above me is correct but for the margin of error, I got 34%, 58% for the 90% interval and 32%, 60% for 95% interval. He just didnt take his margin of errors numbers and times them by 100 to get a percentage, and then round it so you get 12% for 90% and 14% for 95%. Then add and minus 12 percent to the 46% and thats how you get it. Then do the same with 95%

Answer: 7

Step-by-step explanation:

[tex]\sqrt{2x-5}+4 = x[/tex]

[tex]\sqrt{2x-5} = x-4[/tex]   subtracted 4 from both sides

[tex](\sqrt{2x-5})^2 = (x-4)^2[/tex]   squared both sides to eliminate square root

2x - 5 = x² - 8x + 16         expanded right side

       0 = x² - 10x + 21        subtracted 2x and added 5 on both sides

        0 = (x - 3) (x - 7)        factored right side

0 = x - 3     0 = x - 7          applied zero product property

  x = 3          x = 7             solved for x

Check:

x = 3

[tex]\sqrt{2(3)-5}+4 = (3)[/tex]

[tex]\sqrt{1}+4 = 3[/tex]

1 + 4 = 3  

FALSE!  x = 3 is NOT a valid solution

x = 7

[tex]\sqrt{2(7)-5}+4 = (7)[/tex]

[tex]\sqrt{9}+4 = 7[/tex]

3 + 4 = 7  

TRUE! x = 7 IS a valid solution

Answer:

Option 4 is correct.

The equation [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex] is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Step-by-step explanation:'

Given equation: [tex]4x^2 -24x + 4y^2 + 72y = 76[/tex]

First group the terms with x and those with y;

[tex](4x^2-24x)+(4y^2+72y) = 76[/tex]

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒[tex]4(x^2-6x) +4(y+18y) = 76[/tex]

or

[tex]4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76[/tex]

[tex]4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76[/tex]

[tex]4(x-3)^2 + 4(y+9)^2 - 360 =76[/tex]

Add 360 on both sides we get;

[tex]4(x-3)^2 + 4(y+9)^2 =360 +76[/tex]

Simplify:

[tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Therefore, the given equation is equivalent to [tex]4(x-3)^2 + 4(y+9)^2 =436[/tex]

Answer:

$39 did Gavyn get

Step-by-step explanation:

Given the statement: Sarah and Gavyn win some money and share it in the ratio 5:3.

Let the number be x

Then, Sarah win money be 5x  and  Gavyn win money be 3x.

Also, it is given that Sarah gets $26 more than Gavyn.

⇒ 5x = 26 + 3x

Subtract 3x from both sides we get;

5x -3x = 26 + 3x -3x

Simplify:

2x = 26

Divide both sides by 2 we get;

[tex]\frac{2x}{2} = \frac{26}{2}[/tex]

Simplify:

x =13

∵Gavyn win money 3x = 3(13) = $39

Therefore, Gavyn get, $39.

The number of times of the soft drink that refills will be 7.

Inequality is defined as an equation that does not contain an equal sign.

Soft drinks cost $1.89 and refills cost $0.25 each.

With $3.80 to spend on the soft drink and refills.

Then the maximum number of refills will be given as

Let x be the number of refills.

1.89 + 0.25x ≤ 3.80

         0.25x ≤ 1.91

                 x ≤ 7.64

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Brenda will earn $18.75 in interest after 18 months.

To calculate the interest Brenda will earn after 18 months, we can use the simple interest formula:

Principal x Rate x Time = Interest

According to the question, Brenda deposited $500 in a savings account with a simple interest rate of 2.5% per year. Since the time period given is 18 months, we need to convert it to years. 18 months is equivalent to 1.5 years.

Therefore, the interest Brenda will earn after 18 months can be calculated as:

$500 x 0.025 x 1.5 = $18.75

Brenda will earn $18.75 in interest.

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