Sidney made $35 less than four times Casey’s weekly salary. If x represents Casey’s weekly salary, write an expression for Sidney’s weekly salary.

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

Answer:

1-2 yards

Step-by-step explanation:

For most decorative throw pillows you will need 1-2 yards , depending on the size and details you choose to include

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped you plz don't forget to thank me...

Answer:

-1/2 =x

Step-by-step explanation:

4x - 6 = 10x -3

Subtract 4x from each side

4x-4x - 6 = 10x-4x -3

-6 = 6x-3

Add 3 to each side

-6+3 = 6x

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]

Answer:

4√73

Step-by-step explanation:

x^2= 12^2 + 32^2

x^2= 144+ 1024

x^2=1168

x= 4√73

Answer:

Correct option is: Testing a claim about two population means.

Step-by-step explanation:

In this provided scenario, a researchers wants to determine if corporations require a longer work week for the employees "working full-time".

It is given that for many years "working full-time" was 40 hours per week.

The researchers researcher gathers data on the hours that corporate employees work each week.

It is quite clear that the researcher wants to determine whether the number of hours worked per week must be increased from 40 hours or not.

A test for the difference between two population means would help the researcher to reach the conclusion.

Thus, the correct option is: Testing a claim about two population means.

Answer:

1/4

Step-by-step explanation:

1/2 times 1/2

1/2 because there is 3 odds and 3 evens

the total is 6

3/6 equals to 1/2

so 1/2 times 1/2 is 1/4

Answer:

  A.  6.67 in

Step-by-step explanation:

  length/width = 4/3 = x/5

Multiply by 5:

  5(4/3) = x = 20/3 = 6 2/3

The length of the chalkboard is 6.67 inches.

Answer:

s(t)=8t

Step-by-step explanation:

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second.

Let the length of the Square = s

[tex]\dfrac{ds}{dt}=8 $cm/seconds, s_0=0 cm[/tex]

We solve the differential equation above subject to the given initial condition.

[tex]\dfrac{ds}{dt}=8\\ds=8$ dt\\Take the integral of both sides\\\int ds=\int 8$ dt\\s(t)=8t+C, where C is the constant of integration\\When t=0, s=0cm\\s(0)=0=8(0)+C\\C=0\\Therefore, s(t)=8t[/tex]

The formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing is:

s(t)=8t (in cm)

Answer:

Length of the container = 82 cm

Step-by-step explanation:

Given:

Breadth of the container is 40 cm and height of the container is 55 cm

Volume of the container is 180 litres

To find: length of the container

Solution:

A container is in the shape of the cuboid.

Volume of cuboid = length × breadth × height

Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]

(as 1 litre = 1000 [tex]cm^3[/tex] )

Therefore,

[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]

Answer:

B and C

Step-by-step explanation:

The correct option are

B) a cross section of rectangular pyramid perpendicular to the base

C) a cross section of a rectangular prism that is parallel to it's base

Answer:

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

Step-by-step explanation:

The question is incomplete:

Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

                           18–24 25–34 35–55 55 and over Total

Liked Crunchicles   4       9       3 23                  39

Disliked Crunchicles 5        27      28 64              124

No Preference         7        27          10 93                 137

Total                        16        63      41 180            300

One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .

If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.

The number that likes Crunchicles and are 55 and over is 23.

If we calculate the probability as the relative frequency, we have:

[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]

L: Likes Crunchicles.

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

Step-by-step explanation:

You can take the inverse of a function by replacing all x-values in the equation with y-values and vice versa and subsequently solving for y:

Equation given:

[tex]f(x) = \frac{-x}{x+2}[/tex]

Replace all x-values with y and all y-values with x:

[tex]x = \frac{-y}{y+2}[/tex]

Solve for y:

[tex]x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y[/tex]

This is the inverse of f(x), where x ≠ 2..

Answer:

A

Step-by-step explanation:

We can see that Function A's y coordinate doubles every time. The function A = f(x) = 5(2)^x. It is an exponential growth function, and therefore y can never be 0. This means that A does not have an x-intercept.

Function B is a rational function. x cannot be 0, since that would result in an undefined number. This also means that B does not have an x-intercept.

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

Answer:

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.

CHECK THE ATTACHMENT FOR THE GRAPH

EXPLANATION;

FIRST QUESTION:

From the graph maximum profit is the value gotten where p(X) has maximum value, and the maximum value is observed at y- axis at P(X)to be 675.

Thefore, maximum profit the florist will earn from celebration bouquet is $675.

SECOND QUESTION:

Break even is the exact point that profit p(x) is observed as zero.

Checking the given g graph the point where there is zero value of p(X) is observed at x=20 and x= -10 but we can only pick the positive value which is x=20

Therefore, the florist will break even after 20 one- dollar decreases

THIRD QUESTION;

The interval of number of one dollar decreases can be observed at the point where we have the value of P(x) been more than zero, looking at the given graph, the P(x) has its value greater than zero at the interval 0 to 20.Therefore, it can be concluded that the interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)

Answer:

Step-by-step explanation:

Answer:

Another way of saying since the number of baskets scored by team A is 2, and the number of baskets scored by team B is 3, the answer is

C. 2 to 3. :)

Step-by-step explanation:

Answer:

5 one-third ft²

Step-by-step explanation:

rectangle=5ft (base) / 1/3ft (height)

triangle1=3ft (base) / 2ft (height)

triangle2=2/3ft (base) / 2ft (height)

area of rectangle=5x1/3

=5/3ft²

area of triangle1=3x2(1/2)

=3ft²

area of triangle2=2/3x2(1/2)

=2/3ft²

Total area=5/3+6+2/3

=16/3ft² or 5 one-third ft²

Answer:

A

Step-by-step explanation:

took the test on edg 2021

Answer:

[tex]\dfrac{5\pm\sqrt{47}}{6}[/tex]

Step-by-step explanation:

Let's start by setting y to 0 to find the roots of the quadratic.

[tex]x=\dfrac{5\pm \sqrt{25+12}}{6}=\\\\\dfrac{5\pm\sqrt{47}}{6}[/tex]

Hope this helps!

Answer:

4.6%.

Step-by-step explanation:

The probability that a can of paint contains contamination(C) is 3.23%

P(C)=3.23%

The probability of a mixing(M) error is 2.4%.

P(M)=2.4%

The probability of both is 1.03%.

[tex]P(C \cap M)=1.03\%[/tex]

We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]

In probability theory:

[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]

The probability that a randomly selected can has contamination or a mixing error is 4.6%.

Answer:

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]  

Step-by-step explanation:

Information given

n=1100 represent the random sample taken

[tex]\hat p=0.77[/tex] estimated proportion of chips that fall in the first 1000 hours of their use

[tex]p_o=0.76[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Solution

We need to conduct a hypothesis in order to check if the true proportion is equal to 0.76.:  

Null hypothesis:[tex]p=0.76[/tex]  

Alternative hypothesis:[tex]p \neq 0.76[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]  

Answer:

On average it will take 13 hrs 53 minutes before the van is filled

Step-by-step explanation:

The first thing we need to do here is to find find the number of defective light bulbs

Using the poisson process, that would be;

λ * p

where λ is the poisson rate of production which is 300 per hour

and p is the probability that the produced bulb is defective = 0.012

So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour

Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)

What we need to find however is E(X)

Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;

E(X) = r/λ = 50/3.6 = 13.89

Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes

Answer:

When we talk about precision in measurements, we need to mention the significant figures, because that determines the precision.

Specifically, the more significant figures there are, more precise will be the number.

In this case, you can observe that both numbers have the same number of significant figures, which is 3, which means both numbers are equal in precision.

Answer:

Step-by-step explanation:

The given equations are

x + y = 6- - - - - - - - -1

y + z = 6- - - - - - - -2

x + z = 6- - - - - - - - - 3

From equation 2, y = 6 - z

Substituting y = 6 - z into equation 1, it becomes

x + 6 - z = 6

x - z = 6 - 6

x - z = 0

x = z

Substituting x = z into equation 3, it becomes

z + z = 6

2z = 6

z = 6/2

z = 3

x = 3

Substituting x = 3 into equation 1, it becomes

3 + y = 6

y = 6 - 3

y = 3

ax + by + cz = 0

3a + 3b + 3c = 0

3(a + b + c) = 0

Therefore, it is impossible

Answer:D

Step-by-step explanation:

-2=4/5(0)-2

-2=0-2

-2=-2

-6/5=4/5(1)-2

-6/5=4/5-10/5

-6/5=4/5-10/5

-6/5=-6/5

Answer:

His speed as he left the floor is 4.83 m/s.

Step-by-step explanation:

Given: 46 inches = 1.1684 m and mass = 200 lb = 90.7185 Kg.

From the third equation of motion under free fall,

  [tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2gs

Where; V is the final velocity (0), U is the initial velocity (unknown), g is the value of gravity - 10 m/[tex]s^{2}[/tex] and s is the distance = 1.1684 m.

Then;

0 = [tex]U^{2}[/tex] - 2gs

[tex]U^{2}[/tex] = 2gs

   = 2 × 10 × 1.1684

  = 23.368

⇒ U = [tex]\sqrt{23.368}[/tex]

       = 4.8340 m/s

The initial velocity, U = 4.83 m/s.

Therefore, his speed as he left the floor is 4.83 m/s.

Answer:

His speed as he left the floor is 4.83 m/s.

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Complementary means they should sum to 90 degrees

34+56=90

Answer:

True

Step-by-step explanation:

Complementary angles are angles that add to 90 degrees, or a right angle.

If the two angles are complementary, then they will add to 90 degrees.

One angle is 34°, and it's complement is 56°.

Add the angles.

34°+56°

90°

Since they add to 90 degrees, they are complementary angles. Therefore, the statement is true.

Answer:

20-39 => 2

40-59 => 1

60-79 => 1

80-99 => 6

100-119 => 5

Answer: 2, 1, 1, 6, 5

Step-by-step explanation:

20-39

2 | 3

3 | 9

40-59

5 | 0

60-79

7 | 5

80-99

8 | 1 2 4

9 | 3 9 9

100-119

10 | 1 1 5 6

11 | 1

Answer:

x=150 because these are supplementary angles