At an online bookstore, Kendra bought 4 copies of the same book for the members of her book club. She got free shipping because her total was at least $50. What was the minimum price of each book?

Answer:

The expression 6c + 4d - c - 7d can be simplified by combining like terms. 6c + 4d - c - 7d = (6c - c) + (4d - 7d) Simplifying further, we get: 6c + 4d - c - 7d = 5c - 3d So the simplified expression is 5c - 3d.

To simplify the expression 6c + 4d - c - 7d, we can first combine the like terms, which are the terms that have the same variable and the same exponent:

6c - c + 4d - 7d

Simplifying this expression further by combining the like terms, we get:

5c - 3d

Therefore, 6c + 4d - c - 7d simplifies to 5c - 3d.

Rounding to the nearest degree, the direction of u + v is approximately 17°. Therefore, the direction of u + v is 17°.

To find the direction of u + v, we need to first find the components of u and v in the x and y directions:

For vector u:

Magnitude = 50

Direction = 70°

x-component of u = magnitude * cos(direction) = 50 * cos(70°) ≈ 16.225

y-component of u = magnitude * sin(direction) = 50 * sin(70°) ≈ 47.912

For vector v:

Magnitude = 60

Direction = 240°

x-component of v = magnitude * cos(direction) = 60 * cos(240°) ≈ -30

y-component of v = magnitude * sin(direction) = 60 * sin(240°) ≈ -51.961

To find the components of u + v, we add the corresponding components of u and v:

x-component of u + v = 16.225 + (-30) ≈ -13.775

y-component of u + v = 47.912 + (-51.961) ≈ -4.049

The direction of u + v is given by the arctan of the ratio of the y-component to the x-component:

direction of u + v = arctan(-4.049/-13.775) ≈ 16.67°

Rounding to the nearest degree, the direction of u + v is approximately 17°. Therefore, the direction of u + v is 17°.

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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.

However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.

Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.

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Complete Question:

Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,

where did elijah go wrong?

Answer:

\(\frac{8 cupcakes}{1 box}\)

Step-by-step explanation:

All we have to do for this problem is divide.

48 / 6 = 8

There are 8 cupcakes per box.

Answer: 8 cupcakes per box

Step-by-step explanation: "Per box" means in 1 box, so we can rewrite the given statement using fractions as

48 cupcakes/6 boxes = __ cupcakes/1 box.

To find out what goes in the blank, notice that we

have a 1 in the denominator of our second fraction.

So we want to find a fraction that is equivalent

to 48/6 that has a 1 in the denominator.

If we divide the numerator and denominator of 48/6 by 6,

we get the equivalent fraction 8/1 or 8 cupcakes/1 box.

So now we have 8 cupcakes/1 box = __cupcakes/1 box.

So an 8 must go in the blank which means that the unit rate

for 48 cupcakes in 6 boxes is 8 cupcakes per box.

Answer:

No solutions

Step-by-step explanation:

3x+2y-5y=0

3x-3y=0

x=y+10

3(y+10)-3y=0  ==> plugin y+10 for x

3*y + 3*10 - 3y = 0 ==> distribute 3 to y and 10

3y + 30 - 3y = 0

3y - 3y + 30 = 0

30 \(\neq\) 0    

3(y+10)-3y \(\neq\) 0

3(y+10)-3y \(\neq\) 3x-3y  ==> 3x-3y=0

Hence, there are no solutions.

Answer:

\($x_{1}=\frac{3}{2}+\frac{i}{2}\\$\)

\($x_{2}=\frac{3}{2}-\frac{i}{2}$\)

Step-by-step explanation:

It is a Quadratic Equation

\(2x^2-6x+5=0\)

Once it cannot be easily factored, you solve it using the quadratic formula or completing the square. I will use the quadratic formula.

\($x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$\)

\($x=\frac{-(-6)\pm\sqrt{(-6)^2-4\cdot 2\cdot 5}}{2\cdot 2}$\)

The discriminant is negative, therefore we got complex solutions.

\(\Delta= \sqrt{-4}= \sqrt{4i} =2i\)

\($x=\frac{6\pm 2i}{4}$\)

\($x_{1}=\frac{3+i}{2} $\)

\($x_{2}=\frac{3-i}{2} $\)

Now, just rewrite the roots in standard complex form

\($x_{1}=\frac{3}{2}+\frac{i}{2}\\$\)

\($x_{2}=\frac{3}{2}-\frac{i}{2}$\)

Data is displayed in two dimensions using log-log graphs, where both axes have logarithmic scales.

A straight line is depicted on a log-log graph when one variable varies as a constant power of the other. We can determine that X and Y do not have a power law connection if the data points do not form a straight line.

The linear function is equivalently written as log Y = log k + n log X. The statement by John Tukey that "the best thing about being a statistician is that you get to play in everyone's backyard" is amply illustrated by this example.

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Answer:

-45

Step-by-step explanation:

u/3=-15

u=-45

Answer:

x=1/15

Step-by-step explanation:

So we have to subtract 2/5 and 1/3

2/5=6/15 and 1/3=5/15

6/15-5/15=1/15

x=1/15

Answer:

≅236 students

Step-by-step explanation:

Answer:

(1,000 * (100 + 12))/100 = 1,120 - 1,000 = 120 turtles/ per year

Step-by-step explanation:

The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

That's population of turtles in a lake is estimated at 1,000.

And,  The population projected to increase 12% per year.

Hence, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1 + 12/100)¹²ⁿ

⇒ y = 1000 (1 + 0.12)¹²ⁿ

⇒ y = 1000 (1.12)¹²ⁿ

Thus, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

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The surface area of the triangular prism will be 132square cm.

Let h be the height and b be the base of the triangle.

Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = h x b + (L₁ + L₂ + L₃) x W

The right triangular prism is shown.

The third side of the right triangle will be

L₁² = 4² + 3²

L₁² = 16 + 9

L₁² = 25

L₁ = 5

Then the surface area of the triangular prism will be

Surface area = 3 x 4 + (3 + 4 + 5) x 10

Surface area = 12 + 12 x 10

Surface area = 12 + 120

Surface area = 132 square cm

The surface area of the triangular prism will be 132square cm.

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Answer:

5:10 P.M

Step-by-step explanation:

Answer:

5:10 PM

Step-by-step explanation:

3:40 + 1:00 = 4:40

4:40 + 0:30 = 4:70

4:70 = 5:10

Add the time unit, PM.

It's 5:10 PM.

Answer:

y ≥ 118

Step-by-step explanation:

soft pretzels = $4.50

bags of popcorn = $3.25

Let

x = number of soft pretzels sold

y = number of bags of popcorn

The inequality:

4.50x + 3.25y ≥ 1,000

4.50(137) + 3.25y ≥ 1,000

616.50 + 3.25y ≥ 1,000

3.25y ≥ 1,000 - 616.50

3.25y ≥ 383.50

y ≥ 383.50 / 3.25

y ≥ 118

118 bags of popcorn would

need to be sold to make at least $1,000

Answer:

Radius is \(r\approx4.622\,\text{ft}\)

Step-by-step explanation:

\(V=\pi r^2h\\34=\pi r^2(5)\\\frac{34}{5\pi}=r^2\\r=\sqrt{\frac{34}{5\pi}}\\r\approx4.622\,\text{ft}\)

Answer:

2

Step-by-step explanation:

The scale factor can be determined by simplifying the ratio of the corresponding length of the preimage to that of the image.

The preimage is the smaller shape shown, while the image is the lager shape shown.

Any side length can be used.

Thus, length of one side of the preimage, AD = 4 - 1 = 3 units

AD corresponds to side length A'D' if the image = 7 - 1 = 6 units

The ratio of the image length to the ratio of the preimage length = the scale factor

Thus:

6 : 3 = \( \frac{6}{3} = 2 \).

The scale factor is 2.

I'm going to state what I think that the functions were and then answer:

a. \(f(x)=5x^4\) is not exponential.  The variable is not an exponent.

b. \(g(x)=5(17)^x\) IS.  The variable IS an exponent.

c. \(h(x) =11x\) is not.  But if you meant \(h(x)=11^x\) then it is.  Is the variable an exponent?  If so, then the answer is yes.

d. \(j(x)=6(2.56)^x\) IS, assuming again that the variable is an exponent.

e \(k(x) = 4(6)^x\) IS, assuming again that the variable is an exponent.

Now, if any of the x's I wrote as exponents are not exponents, then those are not exponential functions.

Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Answer:

7, 10 and 13.

Step-by-step explanation:

If there are 3  means between 4 and 16 then:

16 is obtained by  adding the common difference 4 times:

(16 - 4)/4 = 12/4 = 3 = common difference.

So the 3 arithmetic means are 4+3, 4 +2*3, 4 + 3(3)

That is 7, 10 and 13.

The smallest possible value for the sum of the 81 draws is 411.

To find the smallest possible value of the sum of the 81 draws, we need to minimize the value of each individual ticket. Since we have six tickets with values of 2, 9, 5, 6, 4, and 4, we can assume that each ticket will be drawn 13 or 14 times (since 13 x 6 = 78 and 14 x 6 = 84).

To minimize the sum of the draws, we want to have as many tickets with a value of 2 and 4 as possible. Let's assume that we have 14 draws for each ticket except for the 9 (which we will assume is drawn 13 times).

So, our calculation would be:

(2 x 14) + (9 x 13) + (5 x 14) + (6 x 14) + (4 x 14) + (4 x 14) = 28 + 117 + 70 + 84 + 56 + 56 = 411

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Based on the test scores of the students, Cindy's z-score on the science test is 2.2

We start by calculating the mean of the scores using:

Mean =Sum/Count

So, we have:

Mean = (75 + 80 + 90 + 100 + 75 + 85 + 80 + 80 + 90 + 85)/10

Mean = 84

Using a statistical calculator, the standard deviation is:

Standard deviation = 7.35

The z-score is then calculated using:

z = (x - mean)/standard deviation

Cindy's score is 100.

So, we have:

z = (100 - 84)/7.35

Evaluate

z = 2.2

Hence, Cindy's z-score on the science test is 2.2

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Find the area of the triangle and multiply by the length of the prism.

Area = 1/2 x 8x3 = 12 square yds.

Volume = 12 x 6 = 72 cubic yards.

No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

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The behavior of the function falls to the left and rises to the right.

Given function  f(x)=x^3-4x^2+7,

Firstly identify the degree of the function which is :

3

Now identify the leading coefficient which is :

1

Now, we know that if the degree is odd then the function ends in opposite direction.

And also the leading coefficient is positive which leads to rise of the graph to the right.

By using the degree and leading coefficient we can determine the behavior of the function by using  below statements ;

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

So the behavior of the function falls to the left and rises to the right.

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Answer:

it will take 5days to reach a total of 180meters

Step-by-step explanation:

80m+20+20+20+20+20

=180meters

=5days

Answer:

yes it is a negative linear funtion

Step-by-step explanation:

Answer: 7 tens and 6 ones

Step-by-step explanation: 76 is two numbers, with a 7 in the tens place and a 6 in the ones place.

76 can be represented as 7 tens and 6 ones or as 6 tens and 16 ones. This involves understanding the place value of digits in a number and knowing that a ten can be broken down into ones.

The number 76 can be broken down into tens and ones in multiple ways. First, let's understand what tens and ones mean in the context of a number. In the number 76, '7' is the tens place, and '6' is the ones place, meaning there are 7 tens (70) and 6 ones (6) making up 76.

One way to show 76 with tens and ones is to say that there are 7 tens and 6 ones. This is a very direct method where we just count the number of tens and ones in the number.

Another way we could break down 76 is to say there are 6 tens and 16 ones. This method involves taking one of the tens and breaking it down into 10 ones, giving us a total of 6 tens and 16 ones.

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Answer:

90%

Step-by-step explanation:

Of his 50 answers, the number that he correctly predicted as being right or wrong is 30 + 15 = 45.

So his accuracy is 45/50 = 90%.

Using it's concept, it is found that the percentage accuracy he had with predicting his scores is 90%.

The percentage of a relative to b is given by:

\(P = \frac{100a}{b}\)

In this problem:

Hence, since he identified 45 out of 50 correctly:

\(P = \frac{100a}{b} = 100\frac{45}{50} = 100(0.9) = 90\%\)

The percentage accuracy he had with predicting his scores is 90%.

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