This is so confusing could anyone help me with this

Rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y = [tex]\frac{5}{4}x+1[/tex].

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

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Answer:

have her do the number times each number every time so if the number is seven and there is a four on top, add or multiply or subtract 7 by 4

Step-by-step explanation:

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

There are numerous ways to define an equation in mathematics. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 2x + 4 = 14, for example, the two expressions 2x + 4 and 14 are separated by the symbol "equal." Mathematical variables are used in even the simplest and most basic mathematical equations.

Here,

the ferris wheel  radius = 10 meters

and he is 14 meters above the ground.

So we can build an equation with given data to find the time todd needed to complete one full rotation around the Ferris wheel

thus time is represented as t

Therefore ,the Ferris wheel rotates at a constant rate so that the angle sweeps out & radians per minute

so speed =8 rad/min

t=distance/speed

t=2[tex]\pi[/tex]/8 min

t=0.785min

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

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Of the following, a sequence which is not a geometric sequence is 3, 6, 9, ... (Option A)

A geometric sequence refers to a sequence in which each term is determined by multiplying the preceding term by the same value which is called the common ratio (r). Hence, the common ratio determined by dividing a term by preceding term is constant in a geometric sequence.

In the given options,

A) r = 6/3 ≠ 9/6

B) r = 9/3 = 27/9 = 3

C) r = 8/4 = 16/8 = 2

D) r = -7/7 =7/-7 = -7/7 = -1

As the common ratio r is constant for option B, C and D, they are geometric sequences. The ratio between consecutive terms is not the same for option A, it is not a geometric sequence.

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Midpoint formula is used to find the centre point of a straight line.

Given :

Let ( x1 , y1 ) and ( x2 , y2) are two points on the straight line.

Midpoint :

The center point of the straight lines with two points is called as midpoint.

Midpoint formula :

( x , y ) = ( x1 + x2 / 2 , y1 + y2 / 2 )

Example :

( x1 , x2 ) = ( 1 , 5 ) and ( y1 , y2 ) = ( 2 , 4 )

( x , y ) = ( 1 + 2 / 2 , 5 + 4 /2 )

= ( 3/2 , 9/2).

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The sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

At the null hypothesis, it is tested if the scores are not different from the regular class, that is, if the mean is of 81.7, hence:

[tex]H_0: \mu = 81.7[/tex]

At the alternative hypothesis, it is tested if the scores are different from the regular class, that is, if the mean is different of 81.7, hence:

[tex]H_1: \mu \neq 81.7[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 9 - 1 = 8 df, hence the critical value is given as follows:

|t| = 2.306.

Thus the decision rule is given as follows:

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are of:

[tex]\overline{x} = 77.2, \mu = 81.7, s = 5.7, n = 9[/tex]

Hence the test statistic is calculated as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{77.2 - 81.7}{\frac{5.7}{\sqrt{9}}}[/tex]

t = -2.37.

|t| > 2.306, hence the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

The problem asks if the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α = .05.

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Answer:

82 degrees

Step-by-step explanation:

due to the resemblance of 90 degrees

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/5-2 [tex]\int\limits^5_2 {x^{2} -8x+10} \, dx[/tex]

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = [tex]\sqrt{x}[/tex] on (1 ,16)

f= 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/16-1 [tex]\int\limits^6_1 {\sqrt{x} } \, dx[/tex]

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

f(x) = [tex]\sqrt{x}[/tex]

f(c) =[tex]\sqrt{c}[/tex]

f(c) = 1/2[tex]\sqrt{c}[/tex]....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = [tex]\sqrt{16}[/tex] -[tex]\sqrt{1}[/tex]/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2[tex]\sqrt{c}[/tex] = 3/15

2[tex]\sqrt{c}[/tex] = 15/3

2[tex]\sqrt{c}[/tex] = 5

[tex]\sqrt{c}[/tex] = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

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The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given as,

A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)

The slope of line AB is given as

m₁ = (7 - 1) / (-2 - 8)

m₁ = 6 / (-10)

m₁ = - 0.6

The slope of line XY is given as

m₂ = (1 - 2) / (-1 + 6)

m₂ = - 1 / (5)

m₂ = - 0.2

The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.

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Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.  A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French. 

There are 3 solutions  to the system of equations

1)single solution

2)infinite solutions

3)no solutions

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

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The given statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants." is true.

The term probability refers the occurrence of a random event.

Here we have given the statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants."

And we have to identify whether this one is true or not.

While looking into the given question, we have identified the value like the following,

level in factor A = 2

levels in factor B = 3

Number of participants = 5

Then the total number of participants is calculated as,

=> (3 + 2)  x 5

Now, we have to expand the given equation, then we get,

=> 5 x 5

Then the total number of participants is 25.

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Answer: x = 56

Step-by-step explanation:

The angle horizontally adjacent from 73 is also equal to 73 due to the triangle being isosceles (the legs are given as equal). Therefore the other angle in that triangle has to be 180 - (73*2) = 34. This angle is a part of the 90 degree angle that is noted in the figure. The other part of that angle must be 90 - 34 = 56. Since this angle is in another isosceles triangle, the angle horizontally adjacent to it must also be 56. x is equal to this angle by definition of vertical angles, so x = 56.

The set of independent variables of a function called the domain of the function.

Domain is the set of values for which the given function is defined.

The set of all possible values of the dependent variable called the range.

The range of a function refers to all the possible values y could be. The formula to find the range of a function is y = f(x). In a relation, it is only a function if every x value corresponds to only one y value.

The set of all possible values for the function called the the domain of the function.

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As the data says , the null and alternate hypothesis will be H0 :p=0.50 and H1:p ≠ 0.50

Let p stand for the true proportion of odds.

To compare the

null hypothesis H0:P = 0.50

alternative hypothesis H1:p 0.50

Let p represent the sample proportion and n represent the sample size.

here,

p = 14/40

= 0.350

n=40, p₀ = 0.500,

= proportional standard error under null 0.50 * (1 -0.50) /40

= 0.079057

The test statistic is as follows:

z = p - p0 / √ p0  ( 1  - p0) / n )

They follow a typical normal distribution under H0

If P-value 0.05 or |Zobs| > 0, we reject H0 t 0.05 threshold of significance. z0.025

Now,

The test statistic value is -1.897367.

1.959964 is the key value.

P-value = 2*P(Z - 1.897367) + P(|z|>Zobs)

= 2 * 0.028890

= 0.057780≈ 0.0578

Because the p-value is greater than 0.05 and |Zobs|  = 1.959964,

As a result, we fail to reject H0 at the 0.05 threshold of significance.

As a result, the population proportion has decreased.

Null and alternate hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always expects no effect or no association between variables, whereas the alternative hypothesis of a test always predicts no effect or no association between variables.

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Answer:

Step-by-step explanation:

Step 1: The sample proportion is pˆ=1440=0.35, the hypothesized proportion is p0=0.5, and the sample size n=40.

Step 2: The test statistic, rounding to two decimal places, is z=0.35−0.50.5(1−0.5)40−−−−−−−−−−√≈−1.897.

Step 3: Since the test is two-tailed and the test statistic is negative, entering the function =2*Norm.S.Dist(−1.90,1) into Excel returns a p-value, rounding to three decimal places, of 0.058.

In 480 ways these 8 people can be seated in a row so that no two software engineers are together

In this question, we need to find the number of ways 8 people can be seated in a row so that no two software engineers are together.

3 software engineers can sit in 3! ways

2 nurses can sit in 2! ways

2 technicians can sit in 2! ways

and a doctor need only one seat

Given that no 2 software engieers are to be seated together.

we first place the 5 people in a row and  software engineers  has to sit between them so no 2 software engieers are to be seated together.

In 6 place they can sit in 6c3 ways and 3 can be combine themself in 3! ways.

Using the formula of combination,

6c3 = 20

so total will be 2 * 2* 1*20*6=480 ways.

Therefore, the number of possible ways = 480

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The radius of convergence is a-R a+R = 6+12 =18 and 6-12 = -6 for the |6x 12/<78 and diverges if |6x 12| 78.

The set of actual numbers x wherein the collection converges is the c program language period of convergence. If there exists a actual wide variety R such that the collection converges for |x−a|R, then R is the radius of convergence.

The radius of convergence is 1/2 of of the duration of the c program language period of convergence. If the radius of convergence is R then the c program languageperiod of convergence will consist of the open c program languageperiod: (a − R, a + R). To discover the radius of convergence, R, you operate the Ratio Test.

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We don't have claim to strength of composite B is smaller than the strength of composite B by at least 2 [N].

From the given data we calculate μ₁s₁ and μ₂s₂ mean and standard deviation of samples A and B respectively.

μ₁ = 464.7, s₁ = 13.42 composite A

μ₂ = 479.49, s₂ = 13.38 composite B

n₁ : n₂ < 30 then we will use t-table.

Null hypothesis  H₀:μ₂-μ₁ ≥ 2

Alternative hypothesis Hₐ : μ₂ - μ₁ < 2

assuming CI 95%

α = 5% = 0.05

and degree of freedom is n₁ + n₂ - 2 = 9 + 9 - 2 = 16

then for the one tail t(c) = 1.746  

now we will compute t(s),

t(s) = (μ₂ - μ₁ - 2)/ sp×√1/n₁ + 1/n₂

sp²= (n₁ - 1) × s₁² + (n₂ - 1) × s₂² / n₁ + n₂ - 2

    = 8 × (13.42)² + 8 × (13.38)²/ 16

     = (8 × 180.1 + 8 × 179) / 16

sp² = 179.55

sp = 13.40

Therefore

t(s) = (479.49 - 464.7 - 2)/ 13.40 ×√1/9+1/9

     = 12.79 / 13.40 × 0.4714

     = 12.79 / 6.32

t(s) = 2.02

t(s) > t(c)

t(s) is rejection region.

Therefore we reject H₀

so we don't have evidence to claim to strength pf composite B is smaller than the strength of composite B at least 2 [N].

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a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).

(b)The P-value is 0.0068.

To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.

A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.

C.I=x-t(alpha/2)xs/sqrt{n}

=3150+_2.01*250/sqrt{50}

=(3078.9358,3221.0642)

b) P value =P(t<-2.83)+P(t>2.83)

use calculator

                 =0.0034+0.0034

                  =0.0068

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The factored form of the equation x² + 3x - 10 is  (x - 2)(x + 5)  .

In the question ,

it is given that ,

the equation is x² + 3x - 10 , we have to express it in factor form ,

So , rewriting the equation by using the split the middle term method .

= x² + 3x - 10

= x² + 5x - 2x - 10     , ...because   5x - 2x = 3x

taking  x common from the first two terms ,

we get ,

= x(x + 5) - 2(x + 5) taking (x+5) common from both the terms ,

we get ,

= (x - 2)(x + 5)

Therefore , the factor form is  (x - 2)(x + 5) .

The given question is incomplete , the complete question is

What is the factored form of x² + 3x - 10  ?

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Answer: 11

Step-by-step explanation:

plug in x where eligible

4(11)-10 and 2(11)+12

both equal 34 and since a triangle's interior angles always equal 180 you can solve for the 3rd angle 32*2= 64 then 180-64= 116

Answer: x=30

Step-by-step explanation:

There's a 90-degree angle given so first do 360-90= 270 which is the retainer of the measures. Then 4x+5x = 9x  so 9x=270

So 270 divided by 9 and 9x divided by 9, to get the x by itself

which equals 30.

As per the given data, the correlation is 0.7.

Correlation:

in statistics, correlation refers the  association between two quantitative variables.

Given,

Here we have the table of data and now we need to find the correlation of the data.

As per the given data we have calculated the value of r as,

X Values

∑ = 132.38

Mean = 5.295

∑(X - Mx)² = SSₓ = 9.005

And the Y Values

∑ = 170.76

Mean = 6.83

∑(Y - My)² = SSₙ = 26.357

When the X and Y Combined

N = 25

∑(X - Mx)(Y - My) = 10.065

So, the R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSₓ)(SSₙ))

r = 10.065 / √((9.005)(26.357)) = 0.6533

Then the Meta Numeric (cross-check)

r = 0.6533

When we round of these value then we get the value of the correlation as 0.7.

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The simplified value of the expression is 23

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

To find the value:

- [ 4 - 3 (-2 + 5)²]

= - [ 4 - 3 (3)²]

= - [ 4 - 3*9]

= - [ 4 - 27]

= - [ -23]

= 23

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The mean tensile strength of the resin cement is between 228.35 and 256.04

Given, a researcher's bounded crowns to 72 extracted teeth.

n = 72, the mean tensile strength of the resin cement,  = 242.2 newtons

The standard deviation, s = 70.6 newton

90% confidence interval for  if the sample size n is 72.

mean = t (8/√n)

Where, α = 0.1 and α/2 = 0.05, (n-1) degrees of freedom = 71

242.2  ± t (8/√n)

242.2 ± 1.664 (8.320)

(228.355 , 256.04)

Lower bound = 228.35N , Upper bound = 256.04N.

Therefore, the Researcher’s are 90% confident level that the mean tensile strength of the resin cement is between 228.35 and 256.04

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Points (0,200) and (200,0) fall outside of the feasible region hence they cannot be the optimal solution.

For the given condition,

Points are (48,84), (0,120), (0,0), (90,0)

The objective function is,

maximize 4X + 10Y

Take point (48, 84), here X = 48 and Y = 84

Substitute values in the objective function equation as shown below;

Z = 4 * 48 + 10 * 84

  = 1032

For point (0,120)

Z = 4 * 0 + 10 * 120

  = 1200

For point (0,0)

Z = 4 * 0 + 10 * 0 =0

For point (90,0)

Z = 4 * 90 + 10 * 0

  = 360

The value of the objective function is maximum at point (0,120). Its value is 1,200.

The viable region does not include points (0,200) and (200,0), hence they cannot be the best option.

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The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes

The time required for Erica to cook her 8 pound roast is 216 minutes

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the time required by Erica to roast 8 pound be = A

Now , the equation will be

Total amount of roast = 5 pound

The time required for Erica to roast 5 pound = 135 minutes

So , the proportion will be

Time required for Erica to roast 5 pound : 5 = Time required by Erica to roast 8 pound : 8

Substituting the values in the equation , we get

135 / 5 = A / 8

Multiply by 8 on both sides of the equation , we get

The value of A = ( 135 x 8 ) / 5

The value of A = 27 x 8

The value of A = 216 minutes

Therefore , the value of A is 216 minutes

Hence , The proportion is 135 : 5 : : A : 8 and the value of A is 216 minutes

The time required for Erica to cook her 8 pound roast is 216 minutes

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1. The number of baseball cards from Gene is 321.

2. An equation that represents finding the number of baseball cards that come from Gene is g = 758 - a.

An equation is a mathematical statement that shows the equality of two or more mathematical expressions.

Equations are solved to solve mathematical problems with unknown variables, combining numbers and variables with mathematical operands.

We depict equations using the equation symbol (=).

The total number of baseball cards with Aaron and Gene = 758

The number of cards from Aaron, a = 437

The number of cards from Gene = g

g = 758 - a.

= 758 - 437

= 321

Thus, using the above equation, we can use the subtraction operation to find that Gene brought 321 baseball cards.

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Answer:

1027

Step-by-step explanation: