average temperatures were measured at five randomly selected soups. the x-bar and r-bar were found 45.25 degree and 1.05 degree, respectively. the uclr and lclr are:

By using the property of similar triangles, it can be obtained that

Value of x is 7.2

What are similar triangles?

Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.

The different axioms of similarity are-

SAS axiom, AA axiom, SSS axiom

By the property of similar triangles,

[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]

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The percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

For the given question.

The statement defining the percentage is ;

28 is 35% of 80.

This can be written as;

35% of 80 = 28

Solve percentage.

35×80/100 = 28

35/100 = 28/80

Or,

28/80 = 35/100

This is the form

a/b = p/100

a = 28

b = 80

p = 35

Thus, the percentage statement 28 is 35% of 80 is written in the form

a/b = p/100 as 28/80 = 35/100.

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The probability that a young adult chosen at random will achieve an IQ between 85 and 160 is 0.8185.

The problem states that;

A typical IQ test result for individuals between the ages of 20 and 34 has a mean of 110 and a standard deviation of 25, and the values are regularly distributed.

To get the probability that a randomly selected young adult will score between 85 and 160 on this IQ test.

Let,

P(85 < x < 160) = P[ (85 - 110)/ 25) < (x - μ) / σ < (160 - 110) / 25) ]

                        = P(-1 < z < 2)

                        = P(z < 2) - P(z < -1)

                        = 0.9772 - 0.1587

                        = 0.8185

Therefore, the probability that a randomly selected young adult will score between 85 and 160 on this IQ test is 0.8185.

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Answer:

g(x)=(-5x+2)+5

Step-by-step explanation:

BC is the common side of both the triangles.

Answer:

BC

Step-by-step explanation:

Common side in both triangles is BC

    Sides of ΔABC,

                   AB ;  BC  and AC

   Sides of ΔDCB,

                  DC, BC and DB

Answer:

you have to add x outside of the parentheses

Step-by-step explanation: hope this helps

Answer:

They all come out to be infinity

Answer:

first and third

Step-by-step explanation:

the equation representing direct proportion is

y = kx ← k is the constant of proportion

y = - 4x is in this form with k = - 4

y = 7x is in this form with k = 7

Answer:

$11.96

Step-by-step explanation:

Now we have to,

→ find 23 percent of $52.

Let's solve the problem,

→ 23% of $52

→ (52/100) × 23

→ 0.52 × 23

→ $11.96

Hence, answer is $11.96.

The equation of the graph in the figure is f(x) = |x - 3| + 5

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

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The property justified by step 4 is after substitution in the equation you get the desired result.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question,

In step 3 substitution of value is taking place.

In step 4 when values are substituted the final result is obtained, so step 4 is the result step.

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Answer:

The answer should be -5/2

Step-by-step explanation:

To find the slope take two plots from the table:

(-2,6) and (0,1)

M= y2-y1 / x2-x1

M= 1-6 / 0--2=-5/2

Answer: 2 + 0.3 +  0.05 + 0.006

Step-by-step explanation: You just have to technically un add the stuff of you understand it that way.

Hope i helped you

Have a great day Darling

Answer:

Step-by-step explanation:

5/6 is closest to 1 and 2/5 is closest to 1/2 so the difference is closest to 1/2.

The solution of the given inequality is when the value of x is greater than or equal 2.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given expression is 3(x-3) -5 (3x-2)≤ 25.

Therefore, the given inequality can be solved as,

3(x-3) - 5(3x-2) ≤ 25

3x - 9 - 15x + 10 ≤ 25

-12x + 1 ≤ 25

-12x ≤ 25 - 1

-12x ≤ 24

x ≥ 2

Hence, the solution of the given inequality is x ≥ 2.

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The simple regression line is used to estimate the population regression line.

We are asked about, the simple regression line

We have options:

a. is estimated by the population regression line.

b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

c. shows the actual (or true) relation between the dependent and independent variables.

d. is used to estimate the population regression line.

e. connects the data points in a sample.

From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.

The simple regression line is used to estimate the population regression line.

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The inequality that needs to be solved is:

3t +270/ 6 ≥ 90.

let we consider that Heidi has 6 subjects in her school.

Therefore, She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.

Now,

To obtain an average first add up all the scores of the tests and then divide by the number of tests.

So far Heidi has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.

If we let each of the three remaining tests each be represent by t, then the sum of all the tests would be:

95 + 92 + 86 + t + t + t

or

273 + 3t

The average of these 6 tests can then be represented by:

3t + 273 / 6

And for her average to be at least 90 then she can get a 90 or more which is the same as ≥ 90

So the inequality that needs to be solved is:

 [tex]\frac{3t + 273}{6}[/tex] ≥ 90

or, [tex]\frac{3 ( t + 91)}{6} \geq 90[/tex]

or, [tex]\frac{t + 91}{2} \geq 90[/tex]

Now, Heidi has to score :

t/2 ≥ 91

or, t/2 ≥ 90

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Answer:

[tex]\left.\dfrac{\text{d}x}{\text{d}t}\right|_{h=2}\approx0.184\; \sf m/s[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Given variables:

Given a = 8.9, use Pythagoras Theorem to create an equation for x² in terms of h²:

[tex]\implies x^2+h^2=a^2[/tex]

[tex]\implies x^2+h^2=8.9^2[/tex]

[tex]\implies x^2+h^2=79.21[/tex]

[tex]\implies x^2=79.21-h^2[/tex]

Differentiate with respect to h:

[tex]\implies 2x\dfrac{\text{d}x}{\text{d}h}=0-2h[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{2h}{2x}[/tex]

[tex]\implies \dfrac{\text{d}x}{\text{d}h}=-\dfrac{h}{x}[/tex]

Given:

[tex]\dfrac{\text{d}h}{\text{d}t}=-0.8\; \sf m/s[/tex]

Therefore:

[tex]\begin{aligned} \dfrac{\text{d}x}{\text{d}t}&=\dfrac{\text{d}x}{\text{d}h}\times \dfrac{\text{d}h}{\text{d}t}}\\\\ \implies &=-\dfrac{h}{x} \times -0.8\\\\ &=\dfrac{0.8h}{x} \end{aligned}[/tex]

Calculate x when h = 2:

[tex]\implies x^2=79.21-2^2[/tex]

[tex]\implies x^2=79.21-4[/tex]

[tex]\implies x^2=75.21[/tex]

[tex]\implies x=\sqrt{75.21}[/tex]

Substitute the values of h and x into the equation for dx/dt:

[tex]\implies \dfrac{\text{d}x}{\text{d}t}=\dfrac{0.8 \times 2}{\sqrt{75.21}}=0.1844939751[/tex]

Therefore, the rate of the ladder's distance from the wall is 0.184 m/s (3 d.p.)

The scale that Wyatt has made use of based on the figures in the question is 1 inch to 0.36 yards.

Building construction would be extremely challenging without a blueprint. You'd be lost without a map! Large objects, such as roads and buildings, can be easily visualized on paper using scale drawings. Scale drawings are even used by a GPS

The scale that Wyatt has used for this drawing is given as:

84 / 231 = 0.36

We would say that for every 1 inch, Wyatt made use of 0.36yards.

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The expectation of getting correct option out of total choice of 5 question.

Probability is the ratio of number of favorable outcomes to the total number of outcomes.It can not be more than 1.

we have five question each of them has four choice, two out of them are correct.

Number of correct choice in one question = 2

Total number of choice in a question = 4

probability to get correct option of one question = 2/4 = 0.5.

Then the probability of 5 question = 5(0.5) = 2.5

Thus, the expectation of correct choice is 2.5.

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For each of the arithmetic sequences, we have that:

a)

b)

c)

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term of the sequence.

For the sequences in this problem, we have that:

Then the general rule is applied to find the nth term of the sequence, while the next two terms are found adding the common ratio.

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The domain and the range of the function are the sets X = {- 9, - 7, - 5, - 3, - 1, 1, 3} and Y = {- 5, - 3, - 1, 1, 3, 5, 7}.

Herein we need to determine the domain and the range of a function, functions are relations such that every element of the domain is related only to one element of the range.

Graphically speaking, the domain of a function are represented by the set of x-coordinates and the range by a set of y-coordinates. The picture shows a discrete function, that is, a function with a finite set of points. Then, the domain and range are listed by the following sets:

Domain

X = {- 9, - 7, - 5, - 3, - 1, 1, 3}

Range

Y = {- 5, - 3, - 1, 1, 3, 5, 7}

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Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

The formula of simple interest is given as

S.I = PRT

We can set up equivalent equations since both interest are equal.

S.I = P(1 + RT)

S.I = 12000(1 + 0.019 * 1)

S.I = 12228

But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal

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The 25 Kg weight will stretch the spring 120.84 cm .

In the question ,

it is given that

the distance(D) that spring  stretches by hanging objects vary directly to the weight(W) of the object .

which means

D ∝ W

to remove the proportionality sign , we write the constant k

So, D = k × W  ,

where k is the constant of proportionality

given that 6 Kg weight stretches the spring 29 cm

So,

29 = k * 6

k = 29/6

to find the stretch for 25 Kg weight

D = (29/6)*25

D = 120.84 cm

Therefore ,The 25 Kg weight will stretch the spring 120.84 cm .

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The probability that the price of the used car is less than $65 is 0.55962.

Here it is given that the price of the used car has a mean of $50 and a variance of $100.

Since it follows normal distribution X~N(μ, σ²)

where,

μ = 50

σ = 100

Here we need to find the probability P(X < 65)
To find this we need to convert the distribution to the standard normal form, N~(0, 1)

We know,

P(X < (x - μ)/ σ) = Φ(Z)

Therefore we get

P(X < (65 - 50)/ 100)

Solving this we get the Z value

= Φ(0.15)

From the Z table, we can get our p-value.

= 0.55962

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The graph shown has two straight lines and the correct equation is

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

y = output variable

m = slope

x = input variable

c = y intercept

interpretation of the equations

4x + y = 6 ⇒ y = -4x + 6

m = -4

c = 6

from the graph only one the lines has the y intercept as 6, also the slope is negative. the line shown by at option (c) the intercept is 6/4 and the slope is positive

−2x + y = −5 ⇒ y = 2x - 5

m = 2x

c = -5

The c is not showing here but it is moving towards negative. the x intercept is showing and we can use it to confirm

y = 2x - 5

0 = 2x - 5

2x = 5

x = 2.5

this coincides with the point on the graph (2.5, 0)

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The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

In the question ,

two points are given as  (-6 , 2) and (-4 , -1) .

we need to find the equation of the line passing through the given points .

to find the equation First we need to find the slope  ,

slope = (-1-2)/(-4-(-6))

slope = -3/(-4 + 6)

slope = -3/2

So , the equation of the line passing through the point (-6 , 2) with slope -3/2 is  

(y - 2) = (-3/2)(x - (-6))

y - 2 = (-3/2)(x + 6)

y - 2 = (-3/2)x - 9

y = (-3/2)x - 9 + 2

y = (-3/2)x - 7

2y = -3x - 14

3x + 2y = -14

Therefore , The equation of the line that passes through the points (-6 , 2) and (-4 , -1) is 3x + 2y = -14 .

The given question is incomplete , the complete question is

Write the equation for the line that passes through the point (-6, 2) and (-4,-1) , write the answer in fully reduced form .

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Answer:

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]

Given equation:

[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]

Simplify using the double angle identities:

[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]

[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]

[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]

[tex]\implies \tan x-2\sin x =0[/tex]

Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):

[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]

Multiply both sides by cos(x):

[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]

[tex]\implies \sin x-2\sin x \cos x=0[/tex]

Factor out sin(x) from the left side of the equation:

[tex]\implies \sin x(1-2 \cos x)=0[/tex]

Apply the zero-product property.

Case 1

[tex]\implies \sin x=0[/tex]

[tex]\implies x=\sin^{-1}(0)[/tex]

[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]

Case 2

[tex]\implies 1-2 \cos x=0[/tex]

[tex]\implies 1=2 \cos x[/tex]

[tex]\implies \cos x=\dfrac{1}{2}[/tex]

[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]

[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]

Solution

[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]