Simplify.
7 (x-1) -2 (x-1)

Answer:

0.279

0.613

-0.44

Step-by-step explanation:

The Zscore that seperates the middle 22% of the distribution ; could be obtained thus. The midpoint is the mean and the probability to either the right or left could be obtained.

To obtain the Zscore that seperates the middle 22% is equivalent to :

The probability to the left of the distribution :

P(x < (0.5 + 0.22/2) = p(x < 0.61)

Using the Z probability calculator :

P(x < 0.61) is equivalent to a Zscore of 0.279

α = 0.27

Z(1 - α) = Z(1 - 0.27) = Z0.73 = p(Z < 0.73) = 0.613

P(x < 0.33) = - 0.44 (Z probability calculator)

Answer:

1 The minimum number of fire extinguishers for Class A hazards for each floor of a building shall be determined by dividing the total floor area by the maximum area to be protected per extinguisher as determined by Table.

Step-by-step explanation:

Answer:

Step-by-step explanation:

148 people

Answer:

Ali has 1528. She has 1146 more cards than Max. In total, there are 1910 cards.

Step-by-step explanation:

382 x 4 = 1528

1528 - 382 = 1146

1528 + 382 = 1910

Answer:

The single plantwide rate, if it is based on machine hours instead of labor hours, is: c.$8.91 per machine hour

Total overheads = Overheads of fabrication department + Overheads of assembly department

Total overheads = $119,400 + $105,300

Total overheads = $224,700

Machine Hours Per  = Blinks + Dinks

Machine Hours Per = (1,158 units×8) + (1995 units× 8)

Machine Hours Per =9264+15,960

Machine Hours Per=25,224 hours

Single plantwide rate = Total overhead / Machine Hours Per

Single plantwide rate= $224,700 /25,224 hours

Single plantwide rate= $8.908 per machine hour

Single plantwide rate=$8.91 per machine hour (Approximately)

Therefore the single plantwide rate, if it is based on machine hours instead of labor hours, is: c.$8.91 per machine hour

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a)Between 27 and 43 mpg: Since this range is within 1 standard deviation of the mean, we can say that approximately 68% of new cars sold have mpg ratings between 27 and 43 mpg.

b)Between 23 and 47 mpg: This range is within 2 standard deviations of the mean, so we can say that approximately 95% of new cars sold have mpg ratings between 23 and 47 mpg.

a. Since we are not assuming a normal distribution, we cannot use the empirical rule to calculate the percentages. However, we can use Chebyshev's theorem, which states that for any distribution (regardless of its shape), at least\(1 - (1/k^2)\) of the data falls within k standard deviations of the mean.

Using Chebyshev's theorem with k=2, we can say that at least \(1 - (1/2^2)\) = 0.75, or 75%, of the data falls within 2 standard deviations of the mean. Therefore:

Between 27 and 43 mpg: Since this range is within 2 standard deviations of the mean, we can say that at least 75% of new cars sold have mpg ratings between 27 and 43 mpg.

Between 21 and 49 mpg: This range is more than 2 standard deviations from the mean, so we cannot use Chebyshev's theorem to make any statements about the percentage of cars in this range.

Within 10 mpg of the mean: Since 10 mpg is less than 2.5 standard deviations from the mean (which is 35 mpg), we can use Chebyshev's theorem with k=2.5 to say that at least\(1 - (1/2.5^2)\) = 0.64, or 64%, of new cars sold have mpg ratings within 10 mpg of the mean.

b. If we assume that mpg ratings for new cars follow a normal distribution, we can use the empirical rule to calculate the percentages of cars sold with mpg ratings between certain ranges. The empirical rule states that for a normal distribution:

Approximately 68% of the data falls within 1 standard deviation of the mean.

Approximately 95% of the data falls within 2 standard deviations of the mean.

Approximately 99.7% of the data falls within 3 standard deviations of the mean.

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Answer:

4s

Step-by-step explanation:

Equate the equations and solve for x:

\(-3x^2 + 24x + 3=-4x^2 + 25x + 15\)

\(\implies x^2 -x -12=0\)

\(\implies x^2 -4x+3x -12=0\)

\(\implies x(x-4)+3(x-4)=0\)

\(\implies (x+3)(x-4)=0\)

\(\implies x=-3, x=4\)

As time is positive, x = 4

The time at which the water balloons collided at their highest point is 7 seconds after the launch.

To find the time at which the two water balloons collided at their highest point, we need to determine the time at which the sum of their heights is maximized. The sum of the heights is represented by the sum of the two quadratic functions.

Given the functions:

y = -3x² + 24x + 3

y = -4x² + 25x + 15

The sum of the heights, S(x), is:

S(x) = (-3x² + 24x + 3) + (-4x² + 25x + 15)

Combine like terms:

S(x) = -7x² + 49x + 18

To find the time when the sum of the heights is maximized, we need to find the x-coordinate of the vertex of the parabolic function S(x). The x-coordinate of the vertex of a quadratic function in the form ax² + bx + c is given by:

x vertex = -b / (2a)

In this case, for S(x) = -7x² + 49x + 18:

a = -7

b = 49

Calculate the x-coordinate of the vertex:

x vertex = -49 / (2 * -7)

x vertex = 7

Now that we have the x-coordinate of the vertex, we can find the corresponding time by plugging it into either of the original functions. Let's use the first function for simplicity:

y = -3x² + 24x + 3

When x = 7:

y = -3(7)² + 24(7) + 3

y = -147 + 168 + 3

y = 24

Therefore, the time at which the water balloons collided at their highest point is 7 seconds after the launch.

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Answer:

c+3d+3

Step-by-step explanation:

The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

Answer:

Part A:

the first step is to work out the brackets by multiplying the coefficients outside the brackets by everything in the brackets.

Part B:

5(3x-4)=-2(6x-9)

15x-20=-12x+18

Part C:

15x-20=-12x+18

15x+12x=18+20

27x/27=38/27

x=1.407

I hope this helps

The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

He needs to borrow: 86667.84

His monthly payment would be: 514.06

He would pay a total of: 185061.6 over the life of the loan

Step-by-step explanation:

roger would need to borrow .72*120372= 86667.84

2.)

calculate the effective rate .059/12= .004916667

\(86667.84=x\frac{1-(1+.004916667)^{-30*12}}{.004916667}\\x=514.0585984\)

which we round to 514.06

3.) he is going to pay a total of 514.06*30*12= 185061.6 over the life of the loan

Step-by-step explanation/answer:

A number c is no less than -1.5 and less than 5.3.

So -1.5<= c < 5.3

You would label your number line and have a filled in closed circle at -1.5 and an open circle at 5.3 to signify that 5.3 is not a possible value of c.

Answer:

Min: 1

Q1: 2
Median: 7
Q3: 9
Max: 11.5

Step-by-step explanation:

The five bars of the box plot correspond (from left-to-right) to the numbers in the five-number summary.

The first bar represents the minimum, which in this case is 1.

The second bar represents the first quartile (Q1), which in this case is 2.

The third bar represents the median, which in this case is 7.

The fourth bar represents the third quartile (Q3), which in this case is 9.

And the fifth bar represents the maximum, which in this case is 11.5.

Answer:

Min: 1

Q1: 2

Median: 7

Q3: 9

Max: 11.5

Step-by-step explanation:

I hope it helps:)

Answer:

Check the answers to the questions below

Step-by-step explanation:

a) If \(\mu_1\) is the average learning rate of the 6th graders without background noise level and \(\mu_2\) is the average learning rate of the 6th graders with background noise level

The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.

Null hypothesis, \(H_0: \mu_1 = \mu_2\)

b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.

Alternative hypothesis, \(H_a: \mu_1 \neq \mu_2\)

c) Assumptions that must be met about the data before she can correctly use independent t-test

There must be random selection of the 6th graders

That the two groups are normally similar in their learning abilities

The division of students into the two groups should be at random

d) She has to  make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.

She can still get accurate results if she include some bias in the selection to prove a particular result.

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Step-by-step explanation:

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If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.

The number of cans which Cole brought = 21 cans of food.

His sister brought in 7 fewer cans than he did, which means she brought in:

⇒ 21 - 7 = 14 cans of food,

Let the total number of food-cans be = "f",

So, the equation to find the number of cans is written as :

⇒ x = 21 + 14,

On adding the number of cans,

We get,

⇒x =  21 + 14 = 35,

Therefore, together they brought in 35 cans of food.

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Question not correct, so i have attached the correct question.

Answer:

SE = 0.59

Step-by-step explanation:

The mean of the students height is;

x' = (53 + 52.5 + 54 + 51 + 50.5 + 49.5 + 48 + 53 + 52 + 50)/10

x' = 51.35

Now, deviation from the mean for each height;

53 - 51.35 = 1.65

52.5 - 51.35 = 1.15

54 - 51.35 = 2.65

51 - 51.35 = -0.35

50.5 - 51.35 = -0.85

49.5 - 51.35 = -1.85

48 - 51.35 = -3.35

53 - 51.35 = 1.65

52 - 51.35 = 0.65

50 - 51.35 = -1.35

Now, square of the deviations above;

1.65² = 2.7225

1.15² = 1.3225

2.65² = 7.0225

-0.35² = 0.1225

-0.85² = 0.7225

-1.85² = 3.4225

-3.35² = 11.2225

1.65² = 2.7225

0.65² = 0.4225

-1.35² = 1.8225

Sum of the squared deviations;

2.7225 + 1.3225 + 7.0225 + 0.1225 + 0.7225 + 3.4225 + 11.2225 + 2.7225 + 0.4225 + 1.8225 = 31.525

Let's divide the sum by the DF of n - 1 i.e 10 - 1 = 9.

Thus;

31.525/9 = 3.50278

Taking the square root of that gives us the standard deviation.

Thus;

s = √3.50278

s = 1.8716

Formula for standard error is;

SE = s/√n

SE = 1.8716/√10

SE = 0.59

Fraction: 5/10

Demical: 0.5

Percent: 50%

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

\(5y +3x= 25\)

\(3y -2x= - 12\)

Step-by-step explanation:

An equation in standard form is:

\(Ax + By = c\\\)

Solving (a):

Given

\(m = -\frac{3}{5}\) --- slope

\(b = 5\) --- y intercept

Required: Determine the equation

An equation has the form:

\(y = mx + b\)

Substitute values for m and b

\(y = -\frac{3}{5}x + 5\)

Multiply through by 5

\(5y = -3x + 25\)

Add  3x to both sides

\(5y +3x= 3x-3x + 25\)

\(5y +3x= 25\)

Solving (b):

Given

\(m = \frac{2}{3}\) --- slope

\(b = -4\) --- y intercept

Required: Determine the equation

An equation has the form:

\(y = mx + b\)

Substitute values for m and b

\(y = \frac{2}{3}x -4\)

Multiply through by 3

\(3 * y = (\frac{2}{3}x -4) * 3\)

\(3y = 2x - 12\)

Subtract 2x from both sides

\(3y -2x= -2x+2x - 12\)

\(3y -2x= - 12\)

Answer:

287.1 inches of the canvas.

Step-by-step explanation:

To solve this, we need to first figure out the total area of the canvas. To do that, multiply width by height.

29*33=957

Now set up your equation for solving for the area of the canvas that the rose covers.

x/957=30/100

We did it where: x is the area of the rose covers, 957 is the amount of inches that the canvas takes up, and the right side of the equation is the percent.

Now cross multiply.

100x=28,710

Now divide both sides by 100.

x=287.1

The red rose covers 287.1 inches of the canvas.

Answer:

Yes. All the conditions for inference have been met.

Step-by-step explanation:

The conditions for inference are:

a) The sample must be random.  The selections of the 30 customers in each Grocery Store were not biased in any way.

b) The sampling distribution must be approximately normal.

c) The observations of the samples were independent.

d) Adequate of sample size.  30 customers represent an adequate sample

e) The variances are not known as they were disclosed in this case.

Answer:

A 573308928

B. 124176266400000000000000000

Four triangles can create a set of pattern blocks that includes a total of four rhombuses.

To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.

To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.

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