3y=21+2(4y-2) solve for y

Answer:

False

Step-by-step explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

95% confidence interval for the mean number of oranges eaten per week per person is 0.8 to 2.6.

This means that we are 95% sure that the true population means for the number of oranges eaten per week per person is 0.8 to 2.6, not that 95% of all people eat between 0.8 and 2.6 oranges per week. So the answer is False.

After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.

We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.

In the prior auction, the following amount of muffins were sold in total:

25 + 12 + 3 + 10 = 50

The percentage of muffins that were wheat muffins is as follows:

25/50 = 0.5

This indicates that wheat muffins accounted for 50% of all sales.

This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:

0.5 x 16 = 8

Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.

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Answer:

Step-by-step explanation:

Volume

V = w h l

V = 2*15*13

V = 390 ft^3

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

Surface area

SA = b*h

SA = 15*13

SA = 195

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

b) Surface area

C) Volume

Answer:  28/9  (choice D)

Explanation:

You don't need a calculator for this.

Each fraction involves 9 in the denominator. The numerators are the only thing that change. Let x be the numerator.

x/9 = 3.1 can be estimated to x/9 = 3 and that solves to x = 27

The numerator is around 27.

Choices A,B,C are ruled out since the numerators are smaller than 28. The only thing left is choice D.

You can use a calculator or long division to confirm that 28/9 = 3.1111... where the '1's go on forever.

Answer:

21cm

Step-by-step explanation:

Add everything together,

The top one is 5cm because of the bottom measurement is the same length

For expression  x+1= √19-x, the value of x is approximately 3.

What exactly are expressions?

In mathematics, an expression is a combination of symbols and operators that represents a quantity or a mathematical relationship. It can contain numbers, variables, operators, functions, and other mathematical symbols. Expressions are used to represent mathematical operations and relationships, and they can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 3x + 2, (x + y) / (x - y), and sin(x) + cos(y).

Now,

Starting with the given equation:

x + 1 = √(19 - x)

We can begin by squaring both sides of the equation to eliminate the square root:

(x + 1)² = (√(19 - x))²

Simplifying the right-hand side:

(x + 1² = 19 - x

Expanding the left-hand side:

x² + 2x + 1 = 19 - x

Moving all the terms to one side:

x² + 3x - 18 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 3, and c = -18:

x = (-3 ± √(3² - 4(1)(-18))) / 2(1)

x = (-3 ± √(81)) / 2

x = (-3 ± 9) / 2

This gives us two solutions:

x = 3 or x = -6

However, we must check both solutions to make sure they are valid in the original equation:

Checking x = 3:

x + 1 = √(19 - x)

3 + 1 = √(19 - 3)

4 = √16

4 = 4

This solution works.

Checking x = -6:

x + 1 = √(19 - x)

-6 + 1 = √(19 + 6)

-5 = √25

-5 ≠ 5

This solution does not work.

Therefore, the solution to the equation x + 1 = √(19 - x) is x = 3.

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Correct question:

What is the solution to the equation below ?

x+1= √19-x

Answer:

Quad 1

Step-by-step explanation:

Answer:

The answer is A Lma/o

Step-by-step explanation:

After the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

The given function is h(x)=x²+7.

The graph of h is translated vertically downward by 7 units, it becomes the graph of a function g.

The new graph of g(x) will have the same shape as the graph of h(x), but it will be shifted down by 7 units. This means that the equation for g(x) can be obtained by subtracting 7 from h(x):

g(x) = x² + 7 -7 = x²

Therefore, after the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

start clearing the x in the first equation

insert this equation into the second one

the system has no solution

The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Answer: After investing for 10 years at 8% interest

Step-by-step explanation: your $10,000 investment will have grown to $21,589 This calculator determines the future value of $10k invested for 10 years at a constant yield of 8.00% compounded annually

Answer:

D - 56

Step-by-step explanation:

Multiply the height, 4 inches, the length, 7 inches, and the width, 2 inches, to get 56.

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Graph is attach below for this question and the equation of this graph is

\(A(x) = 400(1.25)^{x} + 0.\\\)

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

Given that the boat's value increasing at a rate of 25% per year.

So after each year the value becomes = 1 + 25% = 1 + 0.25 = 1.25 of the previous year.

So the equation becomes: \(A(x) = 400(1.25)^{x} + 0.\\\)

Since, b = 1.25 > 1, so A(x) is a increasing function. And for every value of x, A(x) < 0.

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Answer:

She could have saved 1.8 more dollars.

Step-by-step explanation:

30% is the same as 0.3. 0.3 times 54$ is 16.2$. 1/3 times 54$ is 18$. 18$ - 16.2$ is 1.8$.

Answer:

96

Step-by-step explanation:

The least common denominator or lowest common denominator is the smallest multiple that the denominator (that is the number on the bottom of a fraction) has in common.

Since 32, and 3 have no common factors, one simply has to multiply them to find the least common denominator.

32 * 3 = 96

Answer:

2 and 2/3

Step-by-step explanation:

i used my math skillz

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

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Answer:

4

Step-by-step explanation:

Nothing higher than 12 can be a possiblity for 24.

24     1,  2,  3,  4,  6,  8,  12, 24.

32     1, 2,  4,  8,  16

36     1,  2,  3,  4,  6,  9,  12, 18

The one number that shows up the most and at the highest value, is 4. So the GCF is 4

The length of the classroom in feet if the scale model length is 3 inches is 27 feet.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes.

Given:

The scale for the model is 2 inches, which represents 18 feet,

The scale model length 1 inch = 18 \ 2 = 9 feet length

Thus, the length of the classroom having scale model length is 3 inches

 in feet = 9 × 3 = 27 feet

Therefore, the length of the classroom in feet if the scale model length is 3 inches is 27 feet.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Answer: 64% of the variability in weight can be explained by the relationship with height.

Step-by-step explanation:

Here, r= 0.80

\(\Rightarrow\ r^2= (0.80)^2=0.64\)

That means 64% of the variability in weight can be explained by the relationship with height.

The variability in weight is 64 % , explained by the relationship with height.

Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation.

The correlation coefficient is measure the strength of the linear relationship between two variables in a correlation analysis.

Correlation coefficient is represented by r.

Given that, the correlation between height and weight for adults is 0.80.

                   \(r=0.8\)

The variability in weight is, = \(r^{2}=(0.8)^{2} =0.64\)

Thus, the variability in weight is 64 % , explained by the relationship with height.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:

\(0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}\)

In which n is the sample size of the survey.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends.

This means that \(\pi = 0.72\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

Confidence interval:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}\)

The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:

\(0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}\)

In which n is the sample size of the survey.

No, the relationship on the table is not proportional

From the question, we have the following parameters that can be used in our computation:

x   y

____ ____

6 -2

7 -1

8 0

9  1

On the table of values, we can see that:

Using the above as a guide, we have the following:

The relationship is not a proportional relationship

This is so because it does not have a constant rate (addition of 1 to x and y does not represent proportional relationship)

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