If a, b, c, d are positive real numbers such that a, b, c, d form an increasing arithmetic sequence and a, b, d form a geometric sequence, then a/d is
a. 1/12
b. 1/6
c. ¼
d. 1/3
e. ½

If a popular brand of pen is available in 5 colors and 4 writing tips. The  number of different choices of pens do you have with this brand is: 20 choices.

Using this formula to find the number of different choices of pen

Number of different choices of pen = Number of  color × Number of writing tips

Where:

Number of color = 5

Number of writing tips = 4

Let plug in the formula

Number of different choices of pen = 5 × 4

Number of different choices of pen = 20 choices

Therefore the number of different choices of pen  is 20 choices.

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It will grow to $9991.15

A 90% confidence interval for the mean number of children in all household in this city is 1.12 ± 0.328, using formula for confidence interval.

What are mean and standard deviation ?

The standard deviation is a summary measure of the differences of each  observation from the mean.

Formula to calculate confidence interval using mean and deviation:

mean ± Z*(std deviation/√n)

where n = sample size,

Given that :

mean = 1.12

deviation = 2.40

n = 144

We know Z is fixed for 90% confidence i.e. 1.64

So, the confidence interval = 1.12 ± 1.64*(2.4/√144)

                                              = 1.12 ± 1.64 * .2

                                               = 1.12 ± .328

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Derivatives are used to determine that the following is the best statement:

The acceleration of object C is greater than the acceleration of object D.

When you divide the change in velocity by the change in time, you get the acceleration, which is: a=Δv/Δt

In this issue:

hence the right answer is:

The acceleration of object C is greater than the acceleration of object D.

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Answer:

Object C had an acceleration that is greater than the acceleration for D

Step-by-step explanation:

The trade this country will import is given by the option (C) 300 pair of shoes.

The number of shoes exported will be calculated by the formula -

Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.

The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.

Imports = 1300 - 1000

Performing subtraction on Right Hand Side of the equation

Imports = 300

Hence, the import is 300.

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The complete question is attached in figure.

Therefore, the answer to this question is option (C) ex ante forecasts

To face the challenge of improving operational performance while increasing production efficiency, performance forecasting is a crucial service to help decision-making in the idea, design, and operational phases of an asset.

Here,

As to evaluate forecasting performance of a model or compare relative performance of two models,

can be examined on the basis of ex ante forecasts

The term "ex-ante forecast" refers to a forecast that only takes into account the data (i.e., the value of economic variables) that is available at the time of the actual forecast and not the value of some variables that will be available later on.

Therefore, the answer to this question is option (C) ex ante forecasts

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The coordinates of point G are (-8, -10)

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments

The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.

midpoint(M) = (-6, -3)

H = (-4, 4)

let the coordinates of G be (p,q)

taking the x coordinates for M, G and H

-6 = p -4/2

cross multiply

p -4 = -12

p = -12 + 4

p = -8

taking y-coordinates

-3 = q +4/2

q + 4 = -6

q = -6 -4

q = -10

coordinates of G (-8, -10)

in conclusion the coordinates of G is ( -8, -10)

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According to the given area of rectangle, the length and width of the rectangle is 7 and 21 respectively.

Area of rectangle

The standard form of calculating the area of the rectangle is written as,

A = l x w

where l refers the length and w refers the width of the rectangle.

Given,

Here we have given that the area of a rectangle is 147 square feet. And we need to determine the length and width if the length is three times the width.

Let us consider length of rectangle is n,

Then the width of rectangle is 3n.

Here we have to remember that the area of a rectangle is

=> A = n x 3n = 3n²

Here we are told that the area,

=> 3n²=147

Then the value of n² = 49

Therefore, the length is 7 and the width is 21.

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Answer:

The answer is 1.8

Step-by-step explanation:

Let the number be y

So,

y × 5 = 9

5y = 9

Divide both side by 5

5y/5 = 9/5

y = 9/5 = 1.8

Thus, The value of y is 1.8

The required time to travel 30 miles is given as 45 minutes and 3/4 hours.

Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour

Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.

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Answer: conic sections

Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.

The distinction between them is that an integer is a negative number without a decimal point.

All whole numbers and negative numbers are considered integers. This means if we include negative numbers together with whole numbers, we form a set of integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers. In this article, let's learn more about integers, their definition, and their characteristics.

According to our question-

The group of integers that are neither whole nor a natural number are:

As previously noted, the third set of integers lacks a decimal point;

However, the difference between them is that; a negative number without a decimal point is referred to as an integer

From the provided set: only fit into the description of an integer, because

It does not have a decimal point

And that is unfavorable.

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The time taken by the baseball in the air if the ball is not caught is 4.513 seconds.

Here we have to find the time taken by the baseball.

Given data:

The quadratic function is given:

f(x) = 16x² + 70x + 10

To find the value of x we have to formula:

x = ±b [tex]\sqrt{b^{2} - 4ac}[/tex] / 2a

from the equation we get the value of a, b, and c as:

a = -16

b = 70

c = -10

now putting in the equation we have:

x = -70 ±[tex]\sqrt{70^{2} -4(-16)(10)}[/tex] / 2(-16)

  = -70 ±[tex]\sqrt{4900 + 640}[/tex] / -32

  = -70 ± √5540 / -32

  = - 70 ± 74.43 / -32

By calculating this we get two values:

x = -0.138 and 4.513

Time can never be negative so.

x = 4.513

Therefore the time taken is 4.513 seconds.

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Hence, the option D "The interquartile range of the number of DVDs owned is 65" is correct.

In the given question, we have to in each person in a random sample of adults was asked how many DVD, he or she owned.

Summary Statistics are given below

Variable     N     Mean     Median     TiMean     St Dev     St Mean

DVDs         117    129.4       50.0          76.5           3236           29.2

Variable     Minimum        Maximum                    Q1            Q3

DVDs              00                3000                         30.0          95.0

We have to which of the following statements is true?

(A) Seventy-five percent of the adults in the sample own more than 95 DVDs.

(B) Fifty percent of the adults in the sample own between 0 and 129.4 DVDs

(C) The distribution of the number of DVDs owned appears to be approximately symmetric

(D) The interquartile range of the number of DVDs owned is 65.

(E) The distribution of the number of DVDs owned contains outliers on both the low side and the high side.

Option (A) is incorrect because 95 is third quartile value and there is only 25% values above third quartile. So, statement is incorrect.

Option (B) is incorrect because 0 is minimum value and 129.4 is mean value. Percent between mean and minimum is not always fixed, so we cannot say that 50% of values are between 0 and 129.4. So, statement is incorrect.

Option (C) is incorrect because median and mean must be equal for symmetric curve, but these are not equal. So, it is not a symmetric curve.

Option (D) is correct because

IQR (Interquartile range)

IQR = Q3 - Q1

IQR = 95 - 30

IQR = 65.

So, option D is correct answer.

Option (E) is incorrect because

lower outlier limit = Q1-1.5*IQR

lower outlier limit = 30 - 1.5*65

lower outlier limit = -67.5

upper outlier limit = Q3 + 1.5*IQR

upper outlier limit = 95 + 1.5*65

upper outlier limit = 192.5

So, there is outliers only on upper side because maximum is 3000>192.5, but there is not value below 0.

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Therefore , x +3 =y  is the equation which is not the solution of point (3,-1)

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. It is demonstrated that the expressions on the left and right are equivalent to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.

Here,

The given equations are ( a) x-4= y (b) 2x -7 =y (c ) x +3 =y ( d) x/3 = -y

Thus from the given equation

We put, values in each of equation to find that values satisfy the equation or not

Thus, we found  x +3 =y does not satisfy the point (3,-1)

Therefore , x +3 =y  is the equation which is not the solution of point (3,-1)

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The correct question is -

For which of the following equations is (3, - 1) not a solution?

Group of answer choices -      y=x-1, -3x=4y-6, 2y-3x=0, 5x+2y=-16

The answers of the given expressions ordered from least to greatest is

-6, -1, 2, 6, 26

From the question, we are to order the answers of the given expressions from the least to greatest

To do this, we will evaluate the expressions

-13 + 12 = -1

-3 - (-2) + 3

-3 + 2 + 3 = 2

-3 + 9 = 6

9 + (-15)

9 - 15 = -6

13 - (-13)

13 + 13 = 26

Hence, ordering the answers from least to greatest, we get

-6, -1, 2, 6, 26

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Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

The laplace inverse transformation L−1{F(s)G(s)} =  5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]  

If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is

L−1{F(s)} = f(t). (1)

The inverse transform L−1is a linear operator:

L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)

andL−1{cF(s)} = cL−1{F(s)}, (3)

for any constant c

given functions are

f(t) =5t ,g(t) = sin(t)

L(f(t)) = F(s)

L{F(s)*G(s)} = L^-1{5tsin(t)}

   =5L^-1{tsin(t)}

   =5L^-1{[tex]\frac{d}{ds}[/tex] tsin(t)}

    = 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]  

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Answer:

you are right

n=1

Step-by-step explanation:

1/2(-3/2n+1)=3/4-n

-3/4n+1/2=3/4-n

-3/4n+2/4=3/4-4/4n

+3/4n               +3/4n

2/4=3/4-1/4n

-3/4. -3/4

-1/4= -1/4n

/-1/4.  /-1/4

1=n

to check i normally just pop in the value (i know no other way in all my years of school)

1/2(-3/2(1)+1)=3/4-1

1/2(-3/2+1=3/4-1

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

-1/4= -1/4

hopes this helps please mark brainliest

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

By computing the ratio of the vertical to horizontal distance (rise over run) between two points, the slope—a numerical value that defines how steep a line is—is often calculated.

Here,

The slope of line that passes through  (5, 9) and (3, -5)
Slope= gradient between the two points

Slope= (y2-y1)/(x2-x1)

Where y2= -5

Y1= 9

X2= 3

X1= 5

=> (-5-9)/(3-5)

=> -14/-2

=> 7

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

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π√π÷√π  is an irrational number. So option (a) is required answer.

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.

Examples of irrational number: √3, ∛2, π

π is an irrational because it is neither ending nor recurrent.

Solving each part of options, we get

π√π÷√π = π

√25 = 5

√π÷π = 1

2√2 ÷ √2 = 2

As most of the option give rational number only one option gives irrational number which is π

We get π from option (a)

So, option (a) is correct option.

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It is false, the researcher cannot use a z-test for the difference between two proportions.

A hypothesis test was performed to decide whether houses are more prone to being lost to fire than condominiums are. the researcher looked at 1500 randomly selected houses and 1200 randomly selected condominiums over a ten year period. then, since over 30 of each were in the sample, the researcher cannot use a z-test for the difference between two proportions.

z = (X - mean)/(SD/√n)

Where SD is the standard deviation and n is the number of observations.

Here, the required value is not provided. So, we cannot use the z - test.

Therefore, the researcher cannot use a z-test for the difference between two proportions, so the given statement is false.

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The value of the account at the​ child's twenty-first​ birthday is 102125.44

We can use the compound interest formula to determine the value of the account (A) on the​ child's twenty-first​ birthday:

A = P (1 + r/n)^(nt)

Where:

P is the initial amount of money deposited in the account

r is the interest rate

n is the number of times the interest is compounded per year

t is the number of years

Given: P = 14000, r = 9.5% = 0.095, t = 21, n = 12 (i.e. 12 months per year)

Substitututing into A = P (1 + r/n)^(nt):

A = 14000 (1 +  0.095/12)^(12×21)

A = 14000 (1 +  0.095/12)^(252)

A = 102125.44

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a) The linear function for the 2005 estimate is given as follows: y = 30 + 5x.

b) The linear function for the 1990 estimate is given as follows: y = 53.75 + 2.25x.

c) They would be predicted to have the same cost in the year of 2013.

d) The 1990 prediction was closer, however it still had a large residual, hence neither was good enough.

The linear functions are defined in the slope-intercept format, given as follows:

y = mx + b.

In which:

Taking 2005 as the estimate, the function is given as follows:

y = 30 + 5x.

Taking 1990 as the estimate, the equation would be of:

y = 20 + 2.25x.

The estimate for 2005 would be of:

y = 20 + 2.25(15) = 53.75.

Hence the equation taking 2005 as the estimate would be of:

y = 53.75 + 2.25x.

The costs would be the same when:

30 + 5x = 53.75 + 2.25x.

2.75x = 23.75

x = 23.75/2.75

x = 8.63 -> + 2005 -> year of 2013.

The estimates for 2011(6 years after 2005) are given as follows:

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These following answers are correct

We are given residual plots

In given(a) plot there is weak relationship between scatter points

we see curved relationship in this residual plot therefore model is unreasonable .

Note - This model is reasonable when this plot should look approximately normal and scatterplot of residuals should show random

scatter. In these plots we see weak relationship and line as model is unreasonable

2)We are given residual plot.

Given 2nd (c) plot there is strong relationship between scatter points we see positive straigh line relationship in this plot therefore model is resonable.

Also these model look approximately normal land scatterplot of residuals show random scatter.

In these plot we see strong relationship and linear model is reasonable

Therefore, these statements are correct.

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Answer:Pass out the pennies and the dimes to your students. Write a couple of problems on the board that will use regrouping. As you write them, write “ones” over the ones column. Write “tens” over the tens column. Have students take out their coins for each problem.

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is D as

L.H.S.=sin²x sec²x+1

[tex]\frac{sin^2x}{cos^2x} +1\\=\frac{sin^2x+cos^2x}{cos^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]

again

[tex]R.H.S.=tan^2x csc^2x\\=\frac{sin^2x}{cos^2x} \times \frac{1}{sin^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]

L.H.S.=R.H.S.

Any whole number, fraction, or decimal that terminates or repeats is a rational number. Any number that cannot be divided into a fraction and hence does not meet the concept of a rational number is said to be irrational.

When it comes to rationality, we have

r + 2s = c/d and r = a/b.

The result of the substitution is a/b + 2s = c/d

2s= c/d-a/b=(bc-ad)/bd

s = (bc-ad)/2bd

Now that both (bc - ad) and (bd) are integers, bd is not equal to 0

As a result, the integer s is a quotient of the two integers (bc - ad) where bd is not equal to 0. So, s is rational according to the definition. This disproves the idea that s is irrational.

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