What is the surface area of the prism

Piecewise functions are used to represent functions that have several domain intervals.

The difference between both ads is #9

The piecewise function is given as:

\(\mathbf{ f(x) = \left[\begin{array}{ccc}32& &x\le 3\\32 +9(x - 3)&\ &x >3\end{array}\right] }\)

The complete question requires that, we calculate the difference in the cost of a 6-line ad and a 7-line ad.

When \(\mathbf{x = 6}\)

We make use of:

\(\mathbf{f(x) = 32 + 9(x - 3)}\) because \(\mathbf{ x > 3}\) covers x = 6

So, we have:

\(\mathbf{f(6) = 32 + 9(6 - 3)}\)

\(\mathbf{f(6) = 59}\)

When \(\mathbf{x = 7}\)

We make use of:

\(\mathbf{f(x) = 32 + 9(x - 3)}\) because \(\mathbf{ x > 3}\) covers x = 7

So, we have:

\(\mathbf{f(7) = 32 + 9(7 - 3)}\)

\(\mathbf{f(7) = 68}\)

The difference (d) is then calculated by subtracting f(6) from f(7)

\(\mathbf{d = f(7)-f(6)}\)

\(\mathbf{d = 68 - 59}\)

\(\mathbf{d = 9}\)

The difference between both ads is #9

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Answer:

-5/2+-1/2√37≤x≤-5/2+1/2√37

Step-by-step explanation:

Step 1: Find the critical points

-x^2-5x+3=0

For this equation: a=-1, b=-5, c=3

−1x^2+−5x+3=0

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(3)/2(-1)

x=5±√37 /−2

x=-5/2+1/2√37

Step 2: Check intervals in between critical points

x≤-5/2+1/2 √37 (Doesn't work in original inequality)

-5/2+-1/2√37≤x≤-5/2+1/2√37 (Works in original inequality)

x≥-5/2+1/2 √37 (Doesn't work in original inequality)

we know that in parallelogram diagonals bisect each other. So.

TX = VX

c + 30 = 16c

16c - c = 30

15c = 30

c = 30 / 15

c = 2

The value of c should be 2 so that it makes a parallelogram.

Here, on solving the provide question to us, we got to know that - 210 feet represents  = 825/4

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Here,

15 feet represents = 1/8 of an inch

1 feet represents = 1/8 X 15

210 feet represents = 1/8 X 15 X 210 = 825/4

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Answer:

\(x + 8 = - 3 \\ x = - 3 - 8 \\ x = - 11 \\ (d) \\ thank \: you\)

Answer:

1. the growth of a plant given by the amount of food

Step-by-step explanation:

Answer:

2.401 x 10\(^{4}\)

Step-by-step explanation:

24,010 (twenty-four thousand ten) is an even five-digits composite number following 24009 and preceding 24011. In scientific notation, it is written as 2.401 × 104.

pi * d/2 + 5*2+7

It is a half circle

10.99+10+7

27.99

The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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Answer:

it is x=7

x=-1

Step-by-step explanation:

i using the quadratic formula

Step-by-step explanation:

Hey there!!

The equation is;

\( {x}^{2} - 6x + 7 = 0\)

Now, Comparing it with ax^2 + bx + c = 0. we get;

a = 1, b= -6 and c = 7

Use quadratic formula.

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

Put all values.

\(x = \frac{ + 6 + - \sqrt{( { - 6)}^{2} - 4 \times 1 \times 7} }{2 \times 1} \)

Simplify them.

\(x = \frac{6 + - \sqrt{36 - 28} }{2} \)

\(x = \frac{ 6 + - \sqrt{8} }{2} \)

\(x = \frac{6 + - 2 \sqrt{2} }{2} \)

Taking positive (+).

\(x = \frac{6 + 2 \sqrt{2} }{2} \)

Simplifying them.

\(x = \frac{2(3 + \sqrt{2} )}{2} \)

\(x = 3 + \sqrt{2} \)

Now, Taking negative (-).

\(x = \frac{6 - 2 \sqrt{2} }{2} \)

Simplifying them.

\(x = \frac{2(3 - \sqrt{2} )}{2} \)

\(x = 3 - \sqrt{2} \)

Therefore the answer is;

\(x = 3 + \sqrt{2} \: and \: 3 - \sqrt{2} \)

Hope it helps...

Rewrite the radicals using the equivalence of radicals and rational exponents.

Then check which of the expressions are equivalent.

Hence, the expressions in options B and D are equivalent.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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These triangles can be proven congruent by using ASA RULE.

What is congruent triangles and its rules ?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.

Main Body:

In ΔTUV and ΔTWV

VT =VT                 ----(1)

∠VTU=∠TVW      -----(2)

As TUVW is a parallelogram

so, ∠T = ∠U

hence, ∠TVU =∠VTW    ----(3)

taking equation 1, 2,3

therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.

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Answer:

Complex numbers

Step-by-step explanation:

Given

\((5 + i)\) and \((5 - i)\)

Required

Determine what both factors are called

From the list of given options. option "complex numbers" answer the question correctly

This is because when numbers are written in form \(a + bi\) where \(b \neq 0\) and \(i = \sqrt{-1}\);  such a number are referred to as complex number

Some other examples are:

\(-7 + 3i\)

\(2 - 7i\)

\(4 + i\)

And lots more

Answer:

8

Step-by-step explanation:

The square of a number square rooted is the number itself.

The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer:

ghthtf

Step-by-step explanation:

tygtgg

Answer:

According to the Central Limit Theorem, the sampling distribution of sample means would have a mean of 5.4 years.

Step-by-step explanation:

For a normally distributed random variable X, with mean and standard deviation, the sampling distribution of sample means with size n can be approximated to a normal distribution with mean and standard deviation.

As long as n is at least 30, the Central Limit Theorem can also be applied to skewed variables.

We have the following problem:

Answer:

Step-by-step explanation:

The mean of the sampling distribution of sample means can be calculated using the formula:

μM = μ

where μ is the population mean and M is the sample mean.

Thus, μM = μ = 5.4 years.

Therefore, the mean of the sampling distribution of sample means would also be 5.4 years.

Answer:

1/2

Step-by-step explanation:

2-(-1)/9-3

= 3/6

=1/2

Answer:d3dasdadqdasdw

Step-by-step explanation:

Answer:

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 509 MPa with a standard deviation of 17 MPa.

This means that \(\mu = 509, \sigma = 17\)

What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?

This is the p-value of Z when X = 509. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{509 - 509}{17}\)

\(Z = 0\)

\(Z = 0\) has a p-value of 0.5

0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa

Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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Histogram for the following intervals will be,

5-9 (4)

10-14 (3)

15-19 (5)

20-24 (3)

Acc to our question-

hence, histogram will show the values.

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Answer:

The length of side AC is 5 units.

The areas of triangle ABC is 10 square units.

Step-by-step explanation:

From point A (1,3) to point C (1,-2) is 5 units

To check this:

3 - (-2) = 3 + 2 =5

We're subtracting since the point went down (from positive 3 to negative 2)

Now for the area:

Area formula for a triangle: \(\frac{1}{2}\)bh = \(\frac{1}{2}\)⋅b⋅h

We already found the height (length) : 5

The base is from point C (1,-2) to point B (5,-2), which is 4 units

To check this:

5 - 1 = 4

Now that we have found the base and height, Let's solve:

\(\frac{1}{2}\)⋅4⋅5 = \(\frac{1}{2}\)⋅20 = 10

Our area is 10 square units.

Hope that helps :)

A residual plot is a scatterplot in which the residuals (vertical distances between the predicted and actual values) are plotted against the independent variable. A residual is defined as the difference between the predicted value (based on the regression equation) and the actual value.

Residual plots are a valuable tool for checking the adequacy of the model. It helps us check whether the assumptions of linearity, independence, equal variance, and normality are met or not.

The most basic way to create a residual plot is to plot the residuals against the fitted values. If the points in the residual plot are randomly scattered around the horizontal axis, then the assumption of linearity has been met.

If the points show a pattern, such as a curved line, then the assumption of linearity has been violated.To create a residual plot, follow these steps:

Step 1: Estimate the regression equation and obtain the predicted values (ŷ) and residuals (e). ŷ = b0 + b1X

Step 2: Plot the residuals on the vertical axis and the independent variable (X) on the horizontal axis

.Step 3: Look for patterns in the residual plot. If the points are randomly scattered around the horizontal axis, then the assumptions of linearity, independence, equal variance, and normality are met. If there is a pattern, such as a curved line, then the assumptions have been violated. A residual plot can be used to detect outliers, influential observations, and nonlinearity.

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Answer:

87,930 Minutes

Step-by-step explanation:

Let us use unit rates for this question. Let's first draw a table.

Minutes   Mile

45               1

This table represents the relation of Sally walking 1 mile in 45 minutes. Let's put the other data we know of in the table.

Minutes   Mile

45               1

                  1954

To find the number of minutes, we must know that if 1 mile takes 45 minutes, we must multiply the number of minutes, which is 45, by 1954 to get the result desired. Let us do that.

1954*45 = 87,930

Minutes   Miles

45               1

87,930      1954

Therefore it will take Sally 87,930 minutes to walk 1,954 Miles.

I Hope This Helps!

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Answer:

multiply all of them then add all of them then divide by the lowest number

12:1 is the scale factor

3.5 ÷ 3.5 = 1 and 142 ÷ 3.5 =123.5 so 42:123.5 ratio simplified is 12:1

Looking at the question, to find the scale factor we are going to divide 42 by 3.5 which is 12. To check our work we will do 1 times 3.5 which is 42.

Why is it not 147:1? Well, scale factoring means that in two similar geometric figures, the scale factor is the ratio of their corresponding sides, dividing the two corresponding lengths of the sides will gives the ratio

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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Answer:

Step-by-step explanation:

√121 = 11

√900 = √30^2 = 30

∛125 = ∛5^3 = 5

∛729 = ∛9^3 = 9