In a certain high school, historically 40% of graduates will go on to college. This the year graduating class has 120 students a) Find the expected value and standard deviation of the number of these graduates who will go on to college. b) The record number of graduates from a class who go on to college is 58. Using an appropriate approximate method, find the probability that this year's class will beat that record

The monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

What is monthly take home pay?

The amount of money left over after taxes, benefits, and other deductions from a paycheck is known as take-home pay. It is the difference left over after subtracting all gross income deductions.

Let,

Number of hours per week = 46 weeks.

Regular hourly wage up to 40 hours = $15.90

Wage up to 40 hours = 40 x 15.90 = $636

Hours over 40 hours, wage is 1.5 times as much

Wage of hour  41 - 46 = 6 x 1.5 x 15.90 = $143.10

Total weekly wage = 636 + 143.10 = $779.10

Since 1 month = 4.345 weeks.

Therefore,

Monthly wage = Weekly wage x 4.345

                        = 777.10 x 4.345

Monthly wage = $3385.19

Now maximum and assurance = 23% of monthly wage

= 23% of 3385.19

= 0.23 x 3385.10

= $778.59

Therefore,

Monthly take home pay = Monthly wage - Tax

                                        = $3385.19 - $778.59

Monthly take home pay = $2606.6

Hence, the monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

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Answer:

y=x^2 + 1

Step-by-step explanation: the second parabola is only raised by 1 unit up, therefore the entire function shifts upwards by 1.

The perimeter of the parallelogram will be D. 2✓26 i+ 8.

It should be noted that the perimeter of the parallelogram will be calculated by using the formula for distance between point.

For WX, the coordinate are (-2, 4)(2, 4)

d = ✓2 - (-2)² + (4 - 4)²

= ✓16 - 0.

= ✓16

= 4

For XY, this will be illustrated as:

d = ✓(1 - (2)² + (-1 - (4)²

= ✓1² + 5²

= ✓1 + 25.

= ✓26

Since the other sides are parallel, the perimeter of the parallelogram will be:

= 2(4) + 2✓26

= 2✓26 + 8

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If you want to invest $20,000 in a no-load mutual fund with a 6.5% yield then 1300 we earn each year.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The amount to invest is $20,000

Twenty thousand is the investment

and 6.5% is the yield.

We need to find how much we earn in each year.

Convert 6.5% to decimal

6.5/100=0.065

Multiply 0.065 with the 20000

0.65×20000

1300

Hence, we earn 1300 each year as an interest.

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The domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

        |x| = x   |   x ≥ 0

        |x| = -x  |   x < 0

We have the following function -

g(x) = |x +3|

Refer to the graph attached. It can be seen that -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

Therefore, the domain and range of the given function is -

Domain :   (- ∞, + ∞)  or  -∞ < x < +∞

Range :   [0 ∞)  or  0 ≤ y < +∞

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Answer: 210

Step-by-step explanation:

The test statistic for the test of whether the slope is of zero is given as follows:

t = -20.

The equation that gives the test statistic is given as follows:

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

In which the parameters are defined as follows:

The value tested of the slope is of:

[tex]\mu = 0[/tex]

The regression line in this problem is of y = 29.29 - 0.88x, hence the mean slope is of:

[tex]\overline{x} = -0.88[/tex]

The standard error and the sample size are given as follows:

s = 0.22, n = 25.

Then the test statistic is calculated as follows:

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

[tex]t = \frac{-0.88 - 0}{\frac{0.22}{\sqrt{25}}}[/tex]

t = -20.

The problem asks for the test statistic regarding whether the slope assumes a value of zero or different of zero.

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Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

The probability that at least one client will have a food allergy is 0.6323 and the percentage of customers who will have a food allergy is 0.08.

What is probability?

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

As given in the question,

The percentage of customers who will have a food allergy is 0.08

At Ying Ying's bakery,

121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Here, P(x) = probability of getting success in x trials, n= sample size ,p = represents the probability that each event will succeed.

As given, we have

n = 12

p=0.08

Let x is the client will have a food allergy.

Following that, the probability that at least one client will have a food allergy will be:

P(x≥1) = 1 - P(x<1)

= 1 - P(x=0)

= 1 - ¹²C₀(0.08)⁰(1 - 0.08)¹²⁻⁰

= 1 - (1)(0.12)¹²

= 1 - 0.3677

= 0.6323

Hence , the probability that at least one client will have a food allergy will be 0.6323 when the percentage of customers who will have a food allergy is 0.08.

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Complete Question

When a customer places an order at Ying Ying's bakery, there is an 8\%8%8, percent probability that the customer will report a food allergy. One day, 121212 customers place orders at Ying Ying's bakery.

Assuming that each of the 121212 customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?

The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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Answer: ABC and AED are congruent by SSS. SSS is if three sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent. AB and AE are both 7, BC is congruent to ED and CA is congruent to DA because of the tick marks.

Therefore ,the true bearing of the plane and its speed is ∝=-71.9° and 324.31 mph

A thing with both magnitude and direction is called a vector. A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector. From the vector's tail to its head is the direction of motion. According to the definition of a resultant vector, a single vector is one that has the same result as several other vectors taken together.

Here,

To find the true bearing of the plane and its speed.

We find the vector component,

Since  N75°W is same as 95°+90°=165°

Thus,

f(x)=300cos100 +50cos165 = -100.39

f(y)=300sin100 +50sin165= 308.38

next we find resultant

R=[tex]\sqrt{f(x)^{2}+f(y)^{2} }[/tex]

R=[tex]\sqrt{(-100.39)^{2}+(308.38)^{2} }[/tex]

R=[tex]\sqrt{105178.35}[/tex]

R=324.31 mph

The bearing of the plane=> ∝=[tex]tan^{-1}[/tex](308.38/-100.39)

So  ∝=-71.96°

Therefore ,the true bearing of the plane and its speed is ∝=-71.96° and 324.31 mph

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The obtained stress which is acting from every direction is at 45 degree.

The transformation equations will be used to calculate the stresses acting on an inclined element.

(σ x+σ y )/2  =75 MPa

(σ x-σ y )/2  =35 MPa

Tor xy = 28 MPa

sin 2θ = sin 90° = 1          

cos 2θ = cos 90° = 0

Substituting these values into Eqs

σ x1 =(σ x+σ y )/2+ (σ x-σ y )/2 cos2θ+ τxy sin2θ      

= 130 MPa

τ x 1 y 1 =  (σ x-σ y )/sin2θ + τxy cos2θ

σ y 1=  (σ x+σ y )/2- (σ x-σ y )/cos2θ+ τxy sin2θ    

= 47Mpa

Elements of stress

We can easily obtain the stresses acting on all sides of an element oriented at = 45° from these results.

The arrows indicate the true directions of the stresses. Take special note of the shear stress directions, which all have the same magnitude. Also, keep in mind that the sum of the normal stresses remains constant at 150 MPa.

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After solving the equation, the system which has infinitely many solutions will be equal to 2x + y = 3.  Hence, option A is correct.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given equation in the question,

6x + 3y = 9  (i)

The system for  infinitely many solutions will be,

Divide the equation (i) by three,

(6x + 3y)/3 = 9/3

2x + y = 3

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Answer:

A) y + 2x = 3

Step-by-step explanation:

The parameter (the regression coefficient) indicates the degree to which the line slopes upwards or downwards by indicating the amount by which a change in x must be multiplied by the corresponding average change in y, or the amount by which y changes for each unit increase in x.

Understanding Linear Regression Coefficients, A positive coefficient indicates that the mean of the dependent variable tends to rise in tandem with an increase in the independent variable's value. A negative coefficient indicates that the dependent variable tends to decrease as the independent variable rises.

In a regression model, the statistical measure known as R-Squared (also known as R2 or the coefficient of determination) is used to figure out how much of the variance in the dependent variable can be explained by the independent variable. In other words, the goodness of fit, or r-squared, measurement indicates how well the data fit the regression model.

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Answer:

$77.50

Step-by-step explanation:

Since each cookie cake feeds 6, she can buy enough cakes to feed 6, 12, 28, 24, 30, 36, etc. people.

The smallest number above 29 she can feed is 30.

Each cookie cake feeds 6.

30/6 = 5

She needs to buy 5 cookie cakes.

5 × $15.50 = $77.50

The pooled proportion is  [tex]\bar{p}[/tex]=0.64.

The value of test statistic is z=1.614.

In statistical tests, which are formal procedures for drawing inferences or taking choices based on data, two different sorts of conjectures are employed: the null hypothesis and the alternative hypothesis. Based on a sample of the population, the hypotheses are suppositions regarding a statistical model of the population. In order to distinguish between statistical noise and scientific claims, tests, which are fundamental components of statistical inference, are frequently utilized in the interpretation of scientific experimental data. The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance. For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.

Given,

The pooled proportion is:

[tex]\bar{p}[/tex]=(X₁+X₂)/(n₁+n₂)

=(70+90)/(100+150)

=160/250

=0.64

Therefore, the pooled proportion [tex]\bar{p}[/tex]=0.64.

The value of test statistic is:

Test statistic=0.1/0.062

=1.614

Therefore, the value of test statistic is z=1.614.

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Answer: I added a bit more answers the one that answers your question is underlined.

a. Reject H0 when z>1.65

b. p=0.64

c. z=1.614

d. We reject the null hypothesis

Step-by-step explanation:

b. p=[tex]\frac{70+90}{100+150} =\frac{160}{250}=0.64[/tex]

c. z=[tex]\frac{0.70-0.60}{\sqrt{0.64(1-0.64)\sqrt{\frac{1}{100}+\frac{1}{150} } } }[/tex]=1.614

Watching basketball games and liking the flavor of coconut "are" independent events because the probability of a teenager from the group watching basketball games "is not equal to" the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.

Independent events is the events which occur freely of each other. An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.

We observe that the event of watching basketball games does not affect liking the flavour of coconut, hence they are independent events their probabilities are most likely not the same.

Therefore, we use "are" for the first statement to show the two events are independent and "is not equal to" for the probability statement.

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If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

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The value of m+n is 37.

Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. The range for probability varies from 0 to 1.

Let A signify the flipping of the head, and let B signify the flipping of the tail. The event ends when we get 5 heads or 2 tails while flipping.

Then, the outcomes are given by AAAAA, BAAAAA, BB, ABB, AABB, AAABB, AAAABB. The probability of getting a head is 1/2 and a tail is 1/2. The probability of the possible outcomes is 1/32, 1/64, 1/4, 1/8, 1/16, 1/32, and 1/64.

The outcomes with five heads are AAAAA and BAAAAA. The sum of the probabilities of getting 5 heads is,

[tex]\begin{aligned}\frac{1}{32}+\frac{1}{64}&=\frac{2+1}{64}\\&=\frac{3}{64}\end{aligned}[/tex]

And, the sum of all the outcomes is, [tex]\begin{aligned}\frac{1}{32 }+ \frac{1}{64}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}&=\frac{2+1+16+8+4+2+1}{64}\\&=\frac{34}{64}\end{aligned}[/tex]

Let p is the probability that a run of 5 heads will occur before a run of 2 tails. The desired probability p is,  

[tex]\begin{aligned}p&=\frac{\text{number of event}}{\text{total outcome}}\\&=\frac{\frac{3}{64}}{\frac{34}{64}}\\&=\frac{3}{34}\end{aligned}[/tex]

Given, p is of the form m/n. So, m is 3 and n is 34. Then, m+n=3+34=37.

The answer is 37.

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Answer:

[tex]m\angle BDC = 68\textdegree[/tex]

Step-by-step explanation:

Using the given information, we can deduce that angles BDC and ADC are supplementary; their measures add to 180°.

This can be represented by the following equation:

[tex](-7x + 12)\textdegree + (-8x+48)\textdegree = 180\textdegree[/tex]

First, solve for x.

[tex]-15x\textdegree + (12 + 48)\textdegree = 180\textdegree[/tex]

[tex]-15x \textdegree = (180 - 60) \textdegree[/tex]

[tex]-15x\textdegree = 120\textdegree[/tex]

[tex]x\textdegree = -8\textdegree[/tex]

[tex]x = -8[/tex]

Then, substitute x into the expression for BDC.

[tex]m\angle BDC = (-7x+12)\textdegree[/tex]

[tex]m\angle BDC = (-7(-8) + 12)\textdegree[/tex]

[tex]m\angle BDC = (56 + 12)\textdegree[/tex]

[tex]m\angle BDC = 68\textdegree[/tex]

The average price of the stock over the first eight years is 50.69 units / year .

Given :

A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function :

S ( t ) = 37 + 16 e^0.04t.

We find the average value of the stock ,

[tex]f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx[/tex]

[tex]f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx[/tex]

[tex]f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt[/tex]

= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( [tex]e^{-0.04 * 8 }[/tex] - [tex]e^{-0.04 * 0[/tex])

= 50.69 units / year.

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STEP ONE: Get a common denominator.

STEP TWO: Add or subtract the numerators.

STEP THREE: Simplify the result if needed. Notice that eg: 3/27 can be simplified, since the numerator and denominator are both divisible by 3.

And that's all there is to it! Final Answer

3/11 is the probability of choosing an L or an S

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

The given word is SQUIRRELLED.

We need to choose single letter from the word.

We have to find the probability of choosing an L or an S

If we were to select a letter that was either an L or S from eleven letters. 1 of them being an S and 2 of them being an L.

We simply add:1+2/11

Three divided by eleven

3/11

Hence, 3/11 is the probability of choosing an L or an S

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A system of linear inequalities to describe this situation are as follows;

x + y ≤ 100

3x + 5y ≥ 360

x ≥ 20

The system of inequalities has been solved graphically and one possible solution is selling 20 tacos and 80 burritos.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of tacos sold and number of burritos sold respectively, and then translate the word problem into algebraic equation as follows:

Since Henry only has enough supplies to make 100 tacos or burritos, we have;

x + y ≤ 100

Also, Henry sells each taco for $3 and each burrito for $5 and must sell no less than (at least) $360 worth of tacos and burritos each day

3x + 5y ≥ 360

Lastly, Henry must sell no less than (at least) 20 tacos;

x ≥ 20

In conclusion, you should use a graphing calculator to plot the system of linear inequalities as shown in the image attached below.

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Answer:

24 square units

Step-by-step explanation:

1/2 times base times height is the formula for the area of a triangle

the base is 12

the height is 4

1/2(12)(4)

6(4)

24

hopes this helps please mark brainliest

The circumcenter theorem states that the circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle. In other words, the circumcenter is the center of a circle that passes through all three vertices of the triangle.

The circumcenter theorem is a fundamental theorem in geometry and is used in the construction of the circumcenter of a triangle. The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle, and its coordinates can be determined by the coordinates of the triangle's vertices.

This theorem is useful in many applications, such as in: the construction of a triangle from its circumcenter, or in determining the distance between two points. It can also be used to determine the area of a triangle from its three vertices. The circumcenter theorem has been studied for centuries, and it is still an important tool for geometers and mathematicians today.

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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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The volume of the tissue box is 85⅓ cubic inches.

The correct answer option is option D

Volume of the tissue box = Base area of the rectangular prism × Height of the rectangular prism

= 16 square inches × 5⅓ inches

= 85⅓ cubic inches

Therefore, the rectangular prism has a volume of 85⅓ cubic inches

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