Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

Answer:

f(x) = (x + 4)^2 - 5

Step-by-step explanation:

Parent function: f(x) = x^2

To show this in a way that may look more familiar, f(x) = 1(x - 0)^2 + 0

Vertex form: f(x) = a(x - h)^2 + k

We know a = 1, because the slope is the same as the parent function.

Vertex: (h,k)

We can see that the vertex of the graph is (-4, -5)

So h = -4 and k = -5

Now all we need to do is plug the variables into our equation.

f(x) = a(x - h)^2 + k

f(x) = 1(x + 4)^2 - 5

f(x) = (x + 4)^2 - 5

Answer:

f(g(x)) =

[tex] {x}^{6} + 6 {x}^{4} + 8x^{2} + 2[/tex]

Step-by-step explanation:

put g(x) instead of any x in f(x)

[tex] {(x ^{2} + 2) }^{3} - 4( {x}^{2} + 2) + 2[/tex]

Answer:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Step-by-step explanation:

Given

[tex]$$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,[/tex] for some integer k[tex]\}[/tex]

[tex]$$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,[/tex] for some integer k},

[tex]$$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,[/tex] for some integer k},

and

[tex]$$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,[/tex]for some integer k}.

Required

Is [tex]\{0, 1, 2, 3\}[/tex] a partition of Z

Let

[tex]k = 0[/tex]

So:

[tex]$$A _ { 0 } = 4 k[/tex]

[tex]$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0[/tex]

[tex]$$A _ { 1 } = 4 k + 1$$,[/tex]

[tex]A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1[/tex]

[tex]A _ { 2 } = 4 k + 2[/tex]

[tex]A _ { 2} = 4 *0 + 2$$ \to A_2 = 2[/tex]

[tex]A _ { 3 } = 4 k + 3[/tex]

[tex]A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3[/tex]

So, we have:

[tex]\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}[/tex]

Hence:

[tex]\{0, 1, 2, 3\}[/tex] is a partition of Z

Answer:

x=2

Step-by-step explanation:

We have

y = 2x-1

y= 4x-5

Therefore, as 2x-1=y=4x-5, we can say that

2x-1=4x-5

add 1 to both sides to make one side have only x components

2x = 4x-4

subtract 4x from both sides to separate the x components

-2x = -4

divide both sides by -2 to separate the x

x = 2

Answer:

x less than or equal to -5

Step-by-step explanation:

2(x-1) ≥ -12

2x - 2 ≥ -12

2x ≥ -10

x ≥ -5

Answer:

hello!

where are you from ?

Step-by-step explanation:

option 4 is correct ...there is no constant ratio.

Answer:

Each area is equal to half the area of ABCD

Step-by-step explanation:

AX ≅ CY    

In parallelogram, opposite sides are equal.

AB = CD

AX + XB = CY + YD

 CY + XB = CY + YD

          XB = CY + YD - CY

XB  = CY

Both trapezoids have equal area

Area of AXYD + area of BXYC =  area of ABCD        

Answer:

A. )  Each area to equal to half of the area of ABCD

Step-by-step explanation:

Edge 2021

Answer:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{} & {Male} & {Female} & {Pink} & {156} & {72} \ \\ {Yellow} & {104} & {48} \ \end{array}[/tex]

Required

Why [tex]prefers\ pink\ lemonade[/tex] and [tex]female[/tex] are independent

First, calculate [tex]P(pink |\ female)[/tex]

This is calculated as:

[tex]P(pink |\ female) = \frac{n(pink\ \&\ female)}{n(female)}[/tex]

[tex]P(pink |\ female) = \frac{72}{48+72}[/tex]

[tex]P(pink |\ female) = \frac{72}{120}[/tex]

[tex]P(pink |\ female) = 0.6[/tex]

Next, calculate [tex]P(pink)[/tex]

[tex]P(pink) = \frac{n(pink)}{n(Total)}[/tex]

[tex]P(pink) = \frac{156 + 72}{156 + 72 + 104 + 48}[/tex]

[tex]P(pink) = \frac{228}{380}[/tex]

[tex]P(pink) = 0.6[/tex]

So, we have:

[tex]P(pink) = P(pink |\ female) = 0.6[/tex]

Hence, they are independent

Answer:

P(pink lemonade | female) = P(pink lemonade) = 0.6.

Step-by-step explanation:

A

Answer:

y = 8

Step-by-step explanation:

First, we know that the equation for standard deviation is

σ = √((1/N)∑(xₐ-μ)²), with σ being the standard deviation, N being the count of numbers, xₐ being individual values, and μ being the mean. Working backwards, we have

0 = √((1/N)∑(xₐ-μ)²)

Squaring both sides, we get

0 = (1/N)∑(xₐ-μ)²

Since 1/N cannot be 0, we know that

0 = ∑(xₐ-μ)²

Since (xₐ-μ)² can only be ≥0, this means that each value of xₐ-μ must be equal to 0, so

0 = xₐ-μ for each a

xₐ = μ

This leads to the conclusion that each value is equal to the mean, so the mean must be 8.

The mean is equal to the sum / amount of numbers. There are 6 numbers, and the sum is (40+y). The mean is

8 = (40+y)/6

multiply both sides by 6

6*8 = 40+y

48 = 40 + y

This means that

y = 8

Answer:

The equation of the line is y=7x

Answer:

C.) 8 pounds

Hope that can help

Answer:

OP = discount amount × 100 / discount %

Step-by-step explanation:

if I understand this correctly, the actual sale price was 36% (100-64) of the originally marked price.

original price (OP) = 100%

64% of OP = 30

1% of OP = 30/64

OP (100%) = 100 × 30/64

this could be simplified to 100 × 15/32, but this hinders is finding the global formula :

OP = discount amount × 100 / discount %

Answer:  43.1 degrees (choice B)

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

Work Shown:

Use the law of sines

sin(A)/a = sin(C)/c

sin(A)/20 = sin(82)/29

sin(A) = 20*sin(82)/29

sin(A) = 0.68294349

A = arcsin(0.68294349)

A = 43.074088

A = 43.1 degrees

Answer:

43.1°

Step-by-step explanation:

Hello, just finished the quiz and the correct answer is 43.1 degrees.

Answer:

Step-by-step explanation:

Because of the Isosceles Triangle Theorem, the angles across from the congruent sides will be congruent. That means that the angle x also measures 42 degrees.

Step-by-step explanation:

for your 1008 question:

1008/2

504/2

252/2

126/2

63/3

21/3

7/7

1

1008 = 2x2x2x2x3x3x7

1008 = (2^2)×(2^2)x(3^2)×7, so 7 would be the answer because of this

lmk if you need me to elaborate on anything

Answer:

x = 11

Step-by-step explanation:

I assume you want x, so I simply rearranged the terms, subtracted, and simplified.

Answer:

151200

Step-by-step explanation:

We can start by essentially taking off the E at the end, meaning that we want to find all the combinations of

EVANESCENC. We can do this because the combinations will have an E at the end by default.

To solve this, we have to figure out the amount of letters and the amount of each letter. There are 10 letters, with 3 E's, 2 C's, 2 N's, 1 S, 1 V, and 1 A. Using the formula [tex]\frac{n!}{n1!n2!...nk!}[/tex] , with n representing the amount of letters and each subset of n representing the amount of each letters, our answer is

[tex]\frac{10!}{3!2!2!1!1!1!} = \frac{10!}{3!2!2!} = 151200[/tex]

Answer:

[tex]Height = 12cm[/tex]

Step-by-step explanation:

Given

[tex]Volume = 1200cm^3[/tex]

The dimension of the base is:

[tex]Base =10cm[/tex]

[tex]Sides = 13cm[/tex]

See comment for complete question

Required

The height of the base

To do this, we make use of Pythagoras theorem where:

[tex]Sides^2 = (Base/2)^2 + Height^2[/tex]

So, we have:

[tex]13^2 = (10/2)^2 + Height^2[/tex]

[tex]13^2 = 5^2 + Height^2[/tex]

[tex]169 = 25 + Height^2[/tex]

Collect like terms

[tex]Height^2 = 169 - 25[/tex]

[tex]Height^2 = 144[/tex]

Take square roots of both sides

[tex]Height = 12cm[/tex]

Answer:

[tex]{ \tt{ = \frac{7}{9} \div \frac{1 }{3} }} \\ = { \bf{ \frac{7}{9} \times \frac{3}{1} }} \\ = \frac{7}{3} [/tex]

Answer:

[tex]x=43[/tex]

Step-by-step explanation:

Corresponding angles are equal. It is implied that the two angles referred to in the triangles are equal, otherwise they should not be labelled as corresponding.

Therefore, we can set both equations equal to each other:

[tex]2x-5=81^{\circ}[/tex]

Add 5 to both sides:

[tex]2x=86[/tex]

Divide both sides by 2:

[tex]x=\frac{86}{2}=\boxed{43}[/tex]

Answer:

Step-by-step explanation:

x : 100 = 7740 : 98 000 000

x = (7740 * 100)/98 000 000

x = 0.007898 %

A percentage is a hundredth of a number      Then                                                    [tex]\displaystyle\bf \frac{7740}{98\cdot10^6} \cdot100=\frac{387}{49000} \approx 0,00789\%[/tex]                                                      

Answer:

Step-by-step explanation:

Answer:

94 cm^2

Hope it helps!

Answer: D) Increase the sample size and decrease the confidence level.

Step-by-step explanation:

A reduced interval width means that the data is more accurate. This can only be achieved if the sample size is increased because a larger sample size is able to capture more of the characteristics of the variables being tested.

A smaller confidence interval will also lead to a reduced interval width because it means that the chances of the prediction being correct have increased.

Answer:

Step-by-step explanation:

If a point (x, y) is reflected across y = -x, coordinates of the image point will be,

(x, y)→ (-y, -x)

Following this rule,

Vertices of the triangle will be,

(3, 1) → (-1, -3)

(3, -2) → (2, -3)

(6, -3) → (3, -6)

Therefore, image of the given triangle A will be,

(-1, -3), (2, -3) and (3, -6)

Answer:

Probability[(X - μ) < 1.1] = 0.6046

Step-by-step explanation:

Given:

σ² = 64

Mean μ = 34

Find:

Probability[(X - μ) < 1.1]

Computation:

Standard deviation σ = √σ²

Standard deviation σ = √64

Standard deviation σ = 8

Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]

Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]

Using z table

Probability[(X - μ) < 1.1] = 0.6046

Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

Given:

f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0 …………….. (1)

[tex]R_{3}[/tex] = (x) = (e^z /4!)x^4

Since the aim is [tex]R_{3}[/tex](x) < 0.001, this implies that:

(e^z /4!)x^4 < 0.0001 ………………………………….. (2)

Multiply both sided of equation (2) by (1), we have:

e^4x^4 < 0.024 ……………………….......……………. (4)

Taking 4th root of both sided of equation (4), we have:

|xe^(z/4) < 0.3936 ……………………..........…………(5)

Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

Therefore, the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Answer:

Step-by-step explanation:

a)   profits = 30,000 + (30,000 * .05 * years)

P(y) = 30,000 + 1500y

b)  P(15) =  30,000 + 1500*(15)

P(15) = 52,500

the way to do these recurring decimals is by firstly separating the repeating part or recurring part and then multiply it by some power of 10 so we move it to the left, lemme show

[tex]3.5\overline{41}\implies \cfrac{35.\overline{41}}{10}\qquad \stackrel{\textit{say that the repe}\textit{ating part is }~\hfill }{x = \overline{0.41}\qquad \qquad \textit{so that }35.\overline{41}=35+\overline{0.41}=35+x}[/tex]

now, let's multiply that repeating part by some power of 10 that moves the 41 to the left, well, we have two repeating decimals, 4 and 1, so let's use two zeros, namely 100 or 10², thus

[tex]100\cdot x = 41.\overline{41}\implies 100x - 41+\overline{0.41}\implies 100x = 41+x\implies 99x=41 \\\\\\ \boxed{x =\cfrac{41}{99}}\qquad \qquad \textit{so then we can say that}~~\cfrac{35.\overline{41}}{10}\implies \cfrac{35+\frac{41}{99}}{10} \\\\\\ \cfrac{~~\frac{3506}{99}~~}{10}\implies \cfrac{~~\frac{3506}{99}~~}{\frac{10}{1}}\implies \cfrac{3506}{99}\cdot \cfrac{1}{10}\implies \cfrac{3506}{990}\implies \blacktriangleright \stackrel{\textit{which simplifies to}}{\cfrac{1753}{495}} \blacktriangleleft[/tex]

Answer:

A. 96.0 square units

Step-by-step explanation:

The formula for the area of a triangle when we know the side length of two sides and the measure of an included angle of a triangle is given as:

A = ½*a*b*Sin C

Where,

a = 13

b = 15

C = 80°

Plug in the values into the formula

A = ½*13*15*Sin 80

A = 96.0187559

A = 96.0 square units (nearest tenth)

Answer:A

Step-by-step explanation: I took the test