A line with a slope of
4/7 passes through the points (h,10) and (–4,6). What is the value of h?

Answer:  (a 0.35) (b 33.18) (c 2.1) (d 0.0861) (e 0.322) (f 48) (g 5.491) (h 183.372)

Step-by-step explanation: what i did here is just take out the decimal and then multiply then after i put it where it makes more sense.

The Area of Face A is 12 m² and face B is 18 m² and face C is 54 m².

Area is a measure of the amount of space enclosed by a two-dimensional shape or surface. It is a fundamental concept in geometry and is expressed in square units.

We have,

length = 9m

width = 6 m

height = 2m

So, the Area of face A

= l w

= 6 x 2

= 12 m²

and, area of Face B

= 9 x 2

= 18 m²

and, Area of face C

= 9 x 6

= 54 m²

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1. The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

2. The probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) = 0.7724

Given that,

In this question we have 2 question.

1. Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.

We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5-cm) =

We know that,

Mean =μ= 125.2

Standard deviation=σ=2.3

n=25

P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]

=P(z<-1.522)

Using the z-table,

=0.0603

Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

2. Steel rods are produced by a firm. Steel rod lengths have a mean of 168.5 cm and a standard deviation of 1.2 cm, and they are regularly distributed. 24 steel rods are packaged together for shipping.

We have to determine the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) =

We know that,

Mean =μ= 168.5

Standard deviation=σ=1.2

n=24

P(168.3<M<169)= P[168.3-168.5/0.2449<(M-μ)/σ< 169-168.5/0.2449]

=P(-0.817<z<2.042)

=P(z<2.042)-P(z<-0.817)

Using the z-table,

=0.9794-0.2070

=0.7724

Therefore, the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) = 0.7724

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Answer: Line A Is the answer

Answer: the answer is 1.2%

There will be a loss of $6000.

What is loss?

In Maths, Loss share formula is that the formula to calculate the proportion loss happened in any business.

Loss = Cost Price – Selling Price

Main body:

Total unit produced = 1000

cost price of 1 unit = $38

Selling price of 1 unit = $54

profit on 1 unit = $54-$38

profit = $16

total profit on 1000 units = 16*1000

                                         = $16000

After additional cost , cost price = 38+ 33 = $71

cost price after = $81

Profit on 1 unit = $10

profit on 1000 units = 10*1000

                                = $10000

Total profit/ loss after further addition = 16000-10000

therefore , loss of $6000 will be there.

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For the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

As given in the question,

Total number have to pick by a player in a lottery daily game is equal to 3

Numbers  from which player have to pick the three numbers is 0 to 9

Total numbers from which player have to pick the three numbers = 10

Given condition : Order of the number does not matter

Total number of choices to pick three numbers from 0 to 9

= ¹⁰C₃

= ( 10! ) / ( 10 - 3 )! (3!)

= 10! / 7! 3!

= ( 10 × 9 × 8 × 7! ) / ( 7!) ( 3 × 2 × 1 )

= 10 × 3 × 4

=120 choices

Therefore, for the given lottery daily game, total number of choices player have to pick for three numbers from 0 to 9 where order does not matter is equal to 120.

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The best description of the sample selected by the administrator is Stratified Random Sample that is option D is correct.

Stratified Random Sampling is the method of sampling in which data of population or any other demographic study is divided into smaller subgroups or subdivisions and then measurements are carried out. These subdivisions are known as Strata. The subdivisions are made on the basis of the attributes of the people of the population such as their income statement or their educational qualifications. This type of sampling technique is also known as random or quota random sampling technique. This sampling technique is also used in determining the life expectancy data. It allows researchers to develop a sample of a small area that represents the entire area.

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Complete Question:

as part of a demographic study, a college administrator needed to survey a sample of students from the college. from each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey. which of the following is the best description of the type of sample selected by the administrator?

a)cluster sample

b)convenience sample

c)simple random sample

d)stratified random sample

e)systematic random sample

Answer:

4y - 8x = 24

Step-by-step explanation:

4y -8x = 24  Add 8x to both sides

4y = 8x + 24  Divide both sides by 4

y = 2x + 6  

This slope is 2 which would great a line parallel to y = 2x + 9

Desmos is a free program that can help you graph.  See the picture below.  You just type in the equation and it graphs it for you.  Cool

Answer: [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

Divide the boxes among the teachers will result in:

[tex]\frac{30}{12} =\frac{6(5)}{6(2)} =\frac{5}{2}[/tex]

So, each teacher will receive [tex]\frac{5}{2}[/tex] or 2.5 boxes of markers.

ASA congruence postulate says that if the two angles and the included side of a triangle are congruent to two angles and the included side of another triangle then the triangles are congruent. ABC ≅ XYZ

Congruent triangles are those with precisely the same dimensions and appearance. Congruent has the symbol. When the dimensions of one triangle's three sides and three angles match those of another triangle's three sides and three angles, the two triangles are said to be congruent.

Angle-Side-Angle congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below.

According to the ASA criterion, ABC = XYZ because BC = YZ and B = Y and C = Z, respectively. Due to the fact that ABC = XYZ, the third angle (A) and the other two sides (A) of ABC must be equal to the equivalent angle (X) and sides of XYZ.

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The length of the long and short side of Brian's fence in backyard in Detroit is 47 and 25 respectively.

Total length = length of two long sides + length of short side

Let the length of short side be x. So, length of long side = 2x - 3

Keep the values in formula

x + 2 (2x - 3) = 119

Performing multiplication on Left Hand Side

x + 4x - 6 = 119

Rewriting the equation

x + 4x = 119 + 6

Performing addition on both sides of equation

5x = 125

x = 125/5

Performing division on Right Hand Side

x = 25

Length of short side = 25

Length of long side = 2×25 - 3

Length of long side = 50 - 3

Length of long side = 47

Hence, the lengths are 25 and 47.

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The set of whole numbers is closed under addition.

A set is the mathematical model for a collection of different things.

The addition of any two whole numbers always produces another whole number. Therefore, the set of whole numbers is closed under addition.

Hence, The set of whole numbers is closed under addition.

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The 95% confidence interval would be given by (60.554;81.446)  

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population means that sits between an upper and lower interval is frequently stated as a percentage.

Here, we have

Given Data: 92 34 40  105 83 55  56 49 40  76 48 96  93 74 73  78 93 100  53 82

We can calculate the mean and the deviation from these data with the following formulas:

X = ∑ᵃ 1ⁿxₐn

s = √∑ᵃ = 1ⁿ(xₐ - X)²n -1

X = 71  represents the sample mean for the sample  

s=22.35 represent the sample standard deviation

n=20 represents the sample size  

The confidence interval for the mean is given by the following formula:

X ± tα/2 - √n...(1)

In order to calculate the critical value tα/2  we need to find first the degrees of freedom, given by:

df = n - 1 = 20 -1 = 19

Since the Confidence is 0.95 or 95%, the value of α = 0.05 and α/2 = 0.025

and we can use excel, a calculator, or a table to find the critical value. The excel command would be:

tα/2 = 2.09

Now we have everything in order to replace into formula (1):

71 - 2.09- 2.35√20 = 60.554

71 + 2.09- 2.35√20 = 81.446

Hence, the 95% confidence interval would be given by (60.554;81.446).

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The greatest common divisor(GCD) of 10 and 50 is 10.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 10 and 50, we have to find the factors of 10 and 50.

Factors of 10:

1, 2, 5, 10

Factors of 50:

1, 2, 5, 10, 25, 50

From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 50 are 1, 2, 10, and 5.

So, the greatest factor of 10 and 50 is 10.

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The perimeter is 29' and the area is 30 square units

The perimeter

This is the sum of the side lengths

From the question, the side lengths are

Side lengths = 9', 4', 11' and 5'

When these side lengths are added, we have

Perimeter = 9 + 4 + 11 + 5

Evaluate the sum

Perimeter = 29

So, the perimeter is 29'

The area

This is calculated as

Area = 1/2 * Sum of parallel sides * Height

So, we have

Area = 1/2 * (9 + 11) * 3

Evaluate

Area = 30

So, the area is 30 square units

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Phenotypic ratio helps us to predict gene expression in the future generations of organisms. In phenotypic ratio calculations, we map out specific parental alleles and predict the probability of how they will be expressed in their offspring.

Phonotypic ratio is a term that describes probability of finding the patterns and frequency of genetic trait outcomes in the offspring of organisms.

Phenotypic ratio is showing physical expression while the genotypic ratio shows genetic makeup. In complete dominance, the progeny shows the intermediate character of both the parents.

A cross of two hybrid F1 hybrids, heterogeneous for a single trait that displays incomplete dominance is predicted to give a 1:2:1 ratio among both the genotypes and phenotypes of the offspring.  

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ASA congruent triangle stands for Angle-Side-Angle.

According to the question,

We have the following information:

ASA congruent triangle

We know that ASA is a property to prove that two triangles are congruent in the same way the properties are used to prove that two triangles are similar.

ASA stands Angle-Side-Angle which means that two triangles can be congruent if the two angles and one side of one triangle is equivalent to the corresponding two angles and side of the other triangle.

There are other properties to prove two triangles are congruent. For example, there is SSS and SAS.

Hence, ASA congruent triangle stands for Angle-Side-Angle.

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The scatterplot that shows a strong association between two variables even if the correlation is near zero is graph C.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables.

Zero correlation is when there is no linear relationship between the variables been studied. When it is shown on a graph, zero correlation would have no clear linear trend either positive or negative. A linear trend is roughly a straight line. A linear trend is positive if it slopes upward and negative if it slopes downward.

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When the scale factor is greater than 1, the image is larger than the pre-image.

Dilatation is a transformation that modifies a figure's size without changing its shape. Due to dilatation, a figure may grow or shrink. The preimage refers to the first figure in dilatation. It shows an expanded figure. Figures are warped from a fixed point called the center of dilatation.

When you enlarge or reduce a figure, the scale factor indicates how much smaller or larger the result will be.

• When the scaling factor is between 0 and 1, the picture is smaller than the preimage. On a scale of 0 to 1, dilations are referred to as reductions.

• If the scale factor is more than 1, the image is bigger than the preimage. The definition of enlargement is a dilatation with a scale factor higher than 1. Each new point in a dilated figure is denoted by the prime sign, ". As an illustration, point', which denotes "prime," would be the enlarged version of point.

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Answer:

3x+15

Step-by-step explanation:

distribute by multiplying 3 to each term

3(x)+3(5)

3x+15

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By performing a change of units from feet to yards, we will see that the backyard measures 31 yards.

We know that Ricardo measured his backyard and he found that it measured 93 feet, but we want to find this measure in yards, so we need to perform a change of units.

To do it, we will use the relation:

1 yard = 3 feet

Then we can write:

1 = (1 yard)/(3 feet).

Now we have the measure:

93 ft

And we can multiply it by (1 yard)/(3 feet), that is equal to 1, so it does not change the measure, only the units:

93 ft = 93ft*(1 yd/3ft) = 31 ft

The backyard measures 31 ft.

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Radius defines the length between the center and corner point of the circle.

Circle:

Circle means a round shape that has no corners or line segments and it is  a closed curve shape in geometry.

Given,

Here we have to define what is radius

As per the concept of the circle, radius is the half of the diameter.

Where the diameter a line segment through the center of a circle with its ends on the circle's circumference.

And the radius refers the straight line from the center to the circumference of a circle or sphere.

In order to find the radius, simply divide the diameter by 2.

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The product of two numbers is negative. Which statement is true

B and E

How does the law of signs for multiplication work?

For division and multiplication: Positive results are obtained if the symptoms are same. If the signs disagree, the outcome is adverse.

Detailed explanation:

Let a and b be two separate numbers. A and B together have a negative product. The reason why the product of a and b is negative, according to the law of signs for multiplication, is because a and b have distinct signs—one is positive and the other is negative.

which claim is accurate?

A. The two numbers' quotient is a positive number. NO.

B. The two numbers' quotient is negative. YES. The quotient of two numbers with different signs is negative in accordance with the law of signs for division.

C. The quotient cannot be used to infer any conclusions. NO.

D. Both numbers have negative signs. NO.

E. One number has a positive sign, whereas the other has a negative sign. YES.

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The equations that can be used to solve for the length (y) of the rectangular room are:

y(y - 5) = 750

y² - 5y = 750

(y + 25)(y - 30) = 0

The area of a rectangular shape = (length)(width).

Given the following:

Area of rectangular room = 750 square feet.

Length of the room = y

Width of the rectangular room = y - 5 feet

Using the area formula, the equation that we can use to find the value of y would be expressed as follows:

y(y - 5) = 750

Expand

y² - 5y = 750

y² - 5y - 750 = 0

Factorize

(y + 25)(y - 30) = 0

Therefore, the possible equations are:

y(y - 5) = 750

y² - 5y = 750

(y + 25)(y - 30) = 0

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The amount 20% more than 1500 is 1800.

The amount 20% of 1500 is

=20/100 × 1500

=300

NOW,

The amount 20% more than 1500 is

=300 + 1500

=1800

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The null hypothesis for the no difference test is 0 and the alternative hypothesis is 4.905 using the level of significance.

a)null hypothesis (H₀) = 0

Alternative hypothesis (H₀) ≠ 0

t = (d)/√n = 850 × √42 ÷ 1123 = 4.902

b) Now we calculate the degrees of freedom given by:

degrees of freedomf

= n-1

= 42 -1

= 41

Now we can calculate the p value, we have a left tailed test the p value is given by:

p=2× P(t₍₄₁₎>4.905) = 0.00015

We can therefore infer that we can reject the null hypothesis that the difference between the two groups is equal because the p value is less than the significance level indicated.

When there are two samples and the data in one sample can really be paired with observations in the other sample, a paired t-test is used to compare the two population means.

The system of the null and alternate hypothesis for this particular case are:

Null hypothesis: μ₁ - μ₂ = 0

Alternative hypothesis:  μ₁ - μ₂ ≠ 0

Or equivalently

Null hypothesis: (H₀) = 0

Alternative hypothesis: (H₀) ≠ 0

c) now it is calculated that  μ₁ - μ₂ = 0 , hence we can conclude that The standard deviation for the mean for groceries is more than the mean for dining out .

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In general, the duration of a bank's zero-coupon securities with short maturities is lower than the duration of its zero-coupon securities with long maturities.

Bonds with no interest payments are those whose face value is paid back at maturity. The phrase "zero-coupon bond" refers to a bond that does not have so-called coupons or periodic interest payments like conventional bonds do. The investor of the bond receives the bond's par value when it matures. Bonds with zero coupon rates do not accrue interest throughout the course of their lifetime. Instead, buyers purchase zero-coupon bonds at a significant discount to face value, which represents the sum the buyer will get when the bond "matures" or becomes due.

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To find which side of the line on the graph of a linear inequality to shade. Follow the steps-

In order to know which area to shade, first pick a point on the side of the line in your graph. then substitute the x and y values into the inequality. once you get the values, check if the inequality is true at that point. If yes, then you shade that side where the point is in. If not, then you shade the other side.

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