If -3(x+8)= -21, then x = -1.

We have enough data to reject our null hypothesis if the value of our test statistics falls below critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

Given that the population mean is 650, we do a two-tail hypothesis test with a level of significance of 0.025.

Let, μ = population mean

Thus, Null hypothesis, [tex]H_{0}[/tex]:μ= 650.

Alternate Hypothesis, [tex]H_{A}[/tex]:μ≠650

In this case, the population mean is equal to 650, according to the null hypothesis.

The alternative hypothesis, on the other hand, contends that the population mean is not 650.

First things first: the level of significance to be accepted for the two-tailed test is ([tex]\frac{\alpha }{2}[/tex]= [tex]\frac{0.025}{2}[/tex]) = 0.0125 or 1.25%.

Therefore, the following is the decision rule for rejecting a null hypothesis:

We have enough data to reject our null hypothesis if the value of our test statistics falls in the rejection region and is less than the critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

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The translation 3 units to the right and 2 units down the plane will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)

Translation is a transformation technique used to change the position of an object on an y-plane.

For instance translating a coordinate (x, y) into (x-3,y -2) means a shift of the image 3 units to the right and 2 units down the plane. In order to get the corresponding coordinates, we will subtract 3 from the x-coordinates and 2 from the y-coordinates.

Given the coordinate of the triangle DEF as shown;

ΔDEF

D(2, 3),

E(l, 1), and;

F(4, O)

The translation 3 units to the right and 2 units down the plane will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)

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We are required to fill in the solution to the question that we have here.

this is done below

Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b. The area of the base of the cube,

B, is (b)*(b) square units.

The volume of the cube is (b)*(b)*(b) cubic units.

The height of each pyramid, h, is  b/2

b = 2h.

There are 6 square pyramids with the same base and height that exactly fill the given cube.

Therefore, the volume of one pyramid is (1/6)(b)(b)(2h)

or One-third Bh.

This is the term that is used to refer to the shape that is known to have a square base and the base could also be triangular. The parts of the base are known to have a connection at the top of the pyramid.

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answer is in the attachment below :)

goodluck!!

The expression 25p+18(p+4) represents the total amount spent on shirts and pants

The given parameters are:

Shirts = 4 more than pants (p)

Cost of shirt = $18

Cost of pant = $25

The above means that:

p + 4 represents the number of shirts Chris buys, while p represents the number of pants

The terms of the expression 25p + 18(p+4) are

25p and 18(p+4)

This means that:

25p = The total cost of pants

18(p+4) = The total cost of shirts

Hence, the expression 25p+18(p+4) represents the total amount spent on shirts and pants

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Step-by-step explanation:

180(n-2)/n =157.5

180n -360/n=157.5

Cross multiplying

180n -360=157.5n

180n-157.5n=360

22.5n=360

22.5n/22.5=360/22.5

n=16, the number of sides the polygon has is 16

The equation represents a population of 370 animals that increases at an annual rate of 11% is .

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1.

Given that,

A population of 370 animals that increases at an annual rate of 11%

a = 370, r = 11%

[tex]p=a(1+r)^{t}[/tex]

  = [tex]370(1+0.11)^{t}[/tex]

p  =  [tex]370(1.11)^{t}[/tex]

Hence, The equation represents a population of 370 animals that increases at an annual rate of 11% is .

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Answer:

Dimensions will be 4 * 2 cm.

Step-by-step explanation:

l = length of rectangle and w = width

Perimeter = 2l + 2w = 12

l + w = 6.

---> l = 6 - w

Volume of the cylinder

V = πr^2l

w = 2πr

--> r = w/2π

l = 6 -  w so

V = π(w/2π)^ 2 * (6 - w)

---> V =  w^2/4π (6- w)

---> V = 3w^2/ 2π - w^3/4π

Differentiating:

dV/ dw =  6w/ 2π - 3w^2 / 4π

             =   - 3(w - 4)w / 4π

This equals 0 for maximum volume

- 3(w - 4)w / 4π = 0

w = 0 or w = 4

Among all the statements the correct statement is cosec B=4/3 which is last statement.

Given a triangle in which angles are different.

We are required to find the correct statement among the given statements.

We have to take statements one by one and find the trigonometric ratios.

Trigonometric ratios are the ratios which expresses the ratios of the sides of a right angled triangle.

Sin Θ=P/H    

Cos Θ=B/H

Tan Θ=P/B

Cosec Θ=H/P

Sec Θ=H/B

Cot Θ=B/P

When we take angle B then we can find that cot B=5/6.

So the first statement is wrong.

When we take angle C then we can find that cosec C=8/5.

So the second statement is also wrong.

When we take angle C then we can find that cot C=6/5.

So the third statement is also wrong.

When we take angle B then we can find that Cosec B=8/6=4/3

So the fourth statement is correct.

Hence among all the statements the correct statement is cosec B=4/3 which is last statement.

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The graph which represents Charlies distance from her car at different times is indicated as attached. The schedule of her movement is also attached.  This type of graph is called Distance Time Graph.

A distance-time graph can show the distance traveled while an item moves in a straight line.

The gradient of the line in a distance-time graph is equal to the object's speed. The item is travelling more quickly the steeper the line and the larger the gradient.

See the attached for Charlies Distance - Time movements visualized in a graph.

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A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

The correlation coefficient exists as the exact measure that quantifies the power of the linear relationship between two variables in a correlation analysis. A correlation coefficient between average temperature and coat sales exists most likely to be between 0 and -1.

A negative correlation suggests two variables that tend to move in opposite directions. A correlation coefficient of -0.8 or lower displays a strong negative relationship, while a coefficient of -0.3 or lower signifies a very weak one.

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Answer:

0 and -1

Step-by-step explanation:

Got it right on the test.

The correct function that has been represented on the graph is,

f(x) = { 2 if -1 < x ≤ 2 as the values of f(x) for the other two parts, -6 ≤ x ≤ -1 and 2 ∠ x ≤ 6 are (2x+17)/5 and (16-7x)/2 respectively.

This can be broken into three parts :

   y-3/x+1 = 2/5

  5y -15 = 2x +2

  2x - 5y = -17

 y-1/x-2 = -7/2

 2y -2 = -7x + 14

2y + 7x = 16

Thus function becomes

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All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is

{( 0,1) (-1,1)}

{(1,0)(0,1)}

{(1,0)(-1,1)}

A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.

Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.

In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.

A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.

S= (1,0), (0,1), (-1))}

option-1

As, dimension of R²=2, so, Ary set

conists of three vectors cannot be baris for R²

so, option-1 is wrong.

option-2

As, dimention of R2-2.

{(10), (-11)} is a linearly independent

subset of S. so And as, this subset

has 2 vectors so it will as also

span R se, it will be a baris

of IR?

So, option-6 is correct

{(0,1)} is linearly independent subset

option-7

As (LO) has one vector. So, it cannot

Span/generate R so, it also cannot be balis

for R2

of S.

But it cannot span R²

So ut cannot

be a baris of R2

se, option-2 is wrong.

Option-3

AS, {(0,1), (-1,1)} is linearly independent

So, option -7, is wrong.

Answer

[as fox amy KER, (-1,1) K (0,1)] subset of s

And also as dim {(0,1), (-11)}=2

which is same as the dimention of IR2

so {(0,1), (-11)} forms a baris of R2

{(1,0), (0,1), (-11)}

{(1,0)}

So, option-3 is

Connect

option-4

{(1,0), (3, 1)} is standard balis of R2

which is subset of S.

10

[{(1,0), (0,1)}]

So, option-4 is correct.

option-5

{(-11)}

consists of one vertex,

so, ut cannot span R², so, ut cannot

be a baris of R²

9090

LO {(1,0), (-1,1)}]

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A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the graphs (see attachment) of the number of gas-fueled cars that were sold by Roger's car company for the first 8-months since the introduction of electric cars, we can logically deduce that it's much easier to determine the slope of graph A than that of graph B.

This ultimately implies that, it would be best for Roger to use graph A in emphasizing a decrease in the number of gas-fueled cars that were sold.

In conclusion, we can infer and logically deduce that Roger should use graph A for his presentation because the number of gas-fueled cars that were sold appears to decrease on this graph.

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Complete Question:

A car company wants to reduce the use of gas-fueled cars by introducing and promoting the use of electric cars. The graphs below show the number of gas-fueled cars sold, y, for the first eight months since the introduction of electric cars. Both graphs show the same information.

Complete the following sentences.

1. To emphasize the decrease in the number of gas-fueled cars sold, it would be best for Roger to use ______ for his presentation.

2. Roger should use this graph for his presentation because the number of gas-fueled cars sold ______ on this graph.

The winning probability is 1/3.

To find the winning probability:

Therefore, the winning probability is 1/3.

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The solution is,  U={ keys on a keyboard}, could describe U .

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Here, we have,

S is a subset of U,

so all of the elements of S must be also elements of U

If U was {letters}, 4, 9, ? would not belong there

If U was {numbers }, x, y, ? would not belong to U

If U was {punctuation marks }, 4, 9, x, y would not be in U

all the elements of S are in U={ keys on a keyboard}

Answer:  U={ keys on a keyboard}, could describe U.

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The data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

Given five statements:

1)Daily temperature highs for winter in 25 US cities.

2)Daily stock reports from the stock market.

3) Height of flowers.

4) Total points scored by a basketball team the whole season.

We are required to choose a statement whose data is most likely to be normally distributed.

A normal distribution is an arrangement of data set in which most values cluster in the middle of the range and the rest off symmetrically towards either extreme.It is basically a probability distribution that is most likely symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. Its graph is a bell curve.

So,the statement which is likely to be normally distributed is total points scored by a basketball team the whole season.

Hence the data which is most likely to be normally distributed is total points scored by a basketball team the whole season.

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Using the hsd test qcrit = 3.65  

HSD testis used to check differences among sample way for significance. The Tukey's HSD assessments all pairwise variations at the same time as controlling the probability of making one or greater type I errors.

A Tukey-Kramer test lets us check the null speculation of no distinction between the population approach for all pairs of businesses. The Tukey-Kramer check (also known as a Tukey sincere importance test, or Tukey HSD), is carried out in R inside the function.

solution

given;

   using HSD test, the degree of freedom = 16

                                                         and α=0. 05

                                                         groups = 3

                         Hence,                    Qcrit = 3.65    {using HSD table}

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Step-by-step explanation:

so ,

Question 6 :-

5 × (3+4) - 4

first solve the Bracket ......

5 × (7) - 4

after multiplication ......

35 - 4

= 31

so , Answer is 1st one ....

Question 7 :-

8 + 1/2 × (6-2) -1

so , here also solve the Bracket first .....

8 + 1/2 × (4) - 1

after multiplication .....

8 + 2 - 1

after + and - .......

10 - 1

= 9 .......

so , Answer is 2nd one .....

Answer:

Q6: 5 times the sum of 3 and 4, then subtract 4.

Q7: Add 8 to half the difference of 6 and 2, then subtract 1.

Step-by-step explanation:

[tex]5 \times (3 + 4) -4[/tex]

• First of all, we can see that 5 is being multiplied by something, so we can say "5 times...".

• Next we see that the 5 was being multiplied by the sum of 3 and 4, so we can combinedly say "5 times the sum of 3 and 4...".

• And finally, we see that 4 is taken away from the result. Therefore we can say " 5 times the sum of 3 and 4, then subtract 4".

[tex]8 + \frac{1}{2} \times (6-2) -1[/tex]

• Firstly, we can see that 8 is being added to something, so we can say "Add 8...".

• Next, we see that 8 was being added to [tex]\bf \frac{1}{2}[/tex] of something, so we can combinedly say "Add 8 to half of...".

• Then we see that the difference (i.e., result of subtraction) of 6 and 2 was being halved. Therefore we say "Add 8 to half of the difference of 6 and 2...".

• Finally, we can see that 1 is subtracted from the result. Therefore, we can say "Add 8 to half of the difference of 6 and 2, then subtract 1".

Answer:

(3, -3 8/9)

Step-by-step explanation:

Use a slope calculation or a graph to find the slope of the line.

m = (y-y)/(x-x)

m = (-3- -5)/(7- -2)

m = 2/9

Then write the equation of the line. I used point-slope form. (You could use y=mx+b, slope-intercept form, but you'd have to first calculate b as well)

Point-slope form:

y -Y = m(x-X)

y - -3 = 2/9(x- 7)

y + 3 = 2/9(x - 7)

We know the x-coordinate of the point we're looking for is 3. Fill that in as well and calculate the y that goes with it.

y + 3 = 2/9(3-7)

y+3=2/9(-4)

y = -8/9 - 3

y = -3 8/9

In decimal form this is -3.8888repeating

see image.

The point at x=3 on the line between M(7,-3) and N(-2,-5) is (3, -3 8/9).

A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

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

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

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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Answer:

D) 4 8/12

Step-by-step explanation:

To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12

The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x + 5

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = x + 5

The next step is to switch/swap the positions of x and y in the above equation y = x + 5

The equation becomes

x = y + 5

The next step is to make y the subject of the formula in the above equation x = y + 5

The equation becomes

y = x - 5

This is done by subtracting 5 from both sides of the equation.

So, we have:

y = x - 5

Express as an inverse function

f'1(x) = x - 5

Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

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The value of r = 9.078.

pv = nrt. The factor “r” in the ideal gas law equation is known as the “gas constant”. r = [tex]\frac{pv}{nt}[/tex]. The pressure times the volume of a gas divided by the number of moles and temperature of the gas is always equal to a constant number.

so the student weights out .0422 grams of the magnesium metal so from here we can calculate that more's, the magnesium that he used, that is the mass of the magnesium over the more mass, which is .024422 over 24 point. That's equal to about .001758. More so also, it says the magnesium metal is react with excessive hydrochloric acid and produce hydrogen gas. A sample of the hydrogen gas is collected over water in a meter at 22 cecr, the volume of clictic gas is 43.9 and mastic pressure. Is that so using the experimental and collected data calculated are in the percent error? So we know the magnesium react with hydrochloride. The reaction ratio is 1 to 2 and we produce 1. More is the hydrogen and 1. More is magnesium chloride. So from this equatium we know that more of the hydrogen that would be produced in this case is equal to the mass of the magnesium here, that's his .001758 more and set way. There's among hydrogen. The temperature is 32 (degree celcius) which we need to convert the unit into kelvin, so it's actually about field 5.15 kelvin and tells you. The volume of the gas is 43.9 in ml, which is .0439 liter and tells you the pressure of the gas is about 832 millimeter. Mercury, which is a 2 times 13332 plus ca, that's equal to about 110922.24 par. So in this case we know p v = n r t.

r = [tex]\frac{pv}{nt}[/tex]

So p = 110922.24. V = 0.0439 , n = 0.001758 t =  305.15. So let's just do the calculations here.

In this case you will find r=?

Here it's about 9.078.

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Answer:

166

Step-by-step explanation:

If the four lines are tangent to the circle, know that:

NA = KA

AD = LD

LC = MC

MB = NB

The question stated that:

NA = 18 --> KA is also 18

BN = 11 --> MB is also 11

AD = 34 --> LD is also 34

BC = 31 --> MC is 20 (Because BC is BM + MC and BM is 11)

We can just add these numbers.

(18+18) + (11 + 11) + (20+20) + (34+34)

= 36 + 22 + 40 + 68

= 76 + 90

= 166

The perimeter of ABCD is 166.

Answer:

130

Step-by-step explanation:

if 2 tangent segments are drawn to a circle from the same external point then they are congruent, then

AN = AK and KD = DL and  MC = LC

then AN = AK = 18 and

KD = AD - AK = 34 - 18 = 16 , so KD = DL = 16

now BM = BN = 11 , then

AB = AN + BN = 18 + 11 = 29

MC = BC - BM = 31 - 11 = 20 and LC = MC = 20 , so

CD = LC + LD = 20 + 16 = 36

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

Perimeter = AB + BC + CD + AD

                 =  29 + 31 + 36 + 34

                 = 130

Answer:

{(5, 3)}

Step-by-step explanation:

Consider the system :

x + 2y = 11

x - 2y = -1

We notice that :

5 + 2×3 = 11

5 - 2×3 = -1

We conclude that :

(5, 3) is the solution to the system.

The length of the line ed according to the description of the cube is; 8.5.

First, since the shape is a cube, it follows that the diagonal of the top face can be used to determine the length of the sides of the top face.

Therefore , we have; length of each side of the top face;

ag = ge = ef = fa = √288/2 = 6√2.

Also, the diagonal of a to d is; √432 = 12√3.

Hence, the length of ed in the group as evident from the length of sides of the cube's top face in which case,

Consequently, the length of line ed is;√432 × 8.5.

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Answer:

See below

Step-by-step explanation:

Using triangle side rule :  The sum of any two sides must be greater than the third side

.5<x<16.5

The range of possible sizes for side x for given triangle is 0.5<x<16.5.

In the given triangle, one side measures 8.5 units, other side is 8.0 units and third side is x units.

The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides.

Here, the range of x is 8.5-8.0<x<8.5+8.0

0.5<x<16.5

Therefore, the range of possible sizes for side x for given triangle is 0.5<x<16.5.

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Answer:

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

Inequality:

1. Distribute:

2. Multiply:

3. Collect like terms:

4. Addition:

5. Divide both sides by 6:

Interval notation for this solution is:

Answer:

[tex]x < -3[/tex]

Interval notation:  (-∞, 3)

Step-by-step explanation:

Given inequality:

[tex]-4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right) > 8[/tex]

Divide both sides by -4 (remembering to change the direction of the inequality sign, since we are dividing by a negative):

[tex]\implies \dfrac{ -4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right)}{-4} > \dfrac{8}{-4}[/tex]

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x < -2[/tex]

Subtract ⁵/₂ from both sides:

[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x-\dfrac{5}{2} < -2-\dfrac{5}{2}[/tex]

[tex]\implies \dfrac{3}{2}x < -\dfrac{9}{2}[/tex]

Multiply both sides by 2:

[tex]\implies \dfrac{2 \cdot 3}{2}x < -\dfrac{2 \cdot 9}{2}[/tex]

[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2}x < -\dfrac{\diagup\!\!\!\!2 \cdot 9}{\diagup\!\!\!\!2}[/tex]

[tex]\implies 3x < -9[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x}{3} < \dfrac{-9}{3}[/tex]

[tex]\implies x < -3[/tex]

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The magnitude of the larger earthquake is about 1.3 greater than the magnitude of the smaller earthquake.

In physics, significance is defined actually as “distance or quantity.” It depicts the absolute or relative course or size wherein an object moves within the sense of motion. it's miles used to express the scale or scope of something. In physics, importance normally refers to distance or quantity.

Magnitude is described as big in size or very vital. An example of value is the depth of the Grand Canyon. An instance of importance is the dimensions of the trouble of world hunger. (geology) A measure of the amount of energy launched by using an earthquake, as indicated on the Richter scale.

The magnitude is more than a few that characterizes the relative size of an earthquake. value is primarily based on the measurement of the maximum movement recorded with the aid of a seismograph.

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There are 8855 ways in which a 4-member committee be formed from 23 members

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The number of ways that a 4-member committee be formed from 23 members is:

Number of ways = 23! / [(23 - 4)!4!] = 8855 ways

There are 8855 ways in which a 4-member committee be formed from 23 members

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Answer:

The answer is 212,520.

Step-by-step explanation:

This is a permutation, not a combination. So, we need to follow the formula

[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]

Plug in the numbers and solve:

[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]

[tex]nP_{r}= \frac{23!}{19!}\\[/tex]

[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]

[tex]nP_{r}= 212,520[/tex]

Because 212,520 is an answer choice, this is the correct answer.