Which is the most accurate way to estimate 23% of 70?

The company which  has the least expensive cartridge is:

                       LMN office company.

LMN Office Company sells 20 printer cartridges for $240.

This means that the cost of 1 printer cartridge is:  $ 240/20=$ 12

Also, . XYZ Supplies has a box of printer cartridges for $150.

The box contains 12 cartridges.

This means that the cost of 12 cartridge is: $ 150

Hence, cost of 1 printer cartridge is: $ 150/12=$ 12.5

Hence, the company which has the least expensive cartridge is:

            LMN Office Company.

( Since, 12 < 12.5  )

Answer:

Option A is correct that is [tex]360^{\circ}[/tex]

Step-by-step explanation:

We have been given a triangle  we need to tell which one of these is a triangle below to map onto itself.

[tex]360^{\circ}[/tex] rotation is the complete rotation which eventually leads to the same figure which is given.

Option A is correct that is [tex]360^{\circ}[/tex] that will cause the triangle below to map onto itself.

Step 1

Find the slope of the given line

Let

[tex]A(-4,4)\ B(4,-2)[/tex]

we know that

the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-2-4}{4+4}[/tex]

[tex]m=\frac{-6}{8}[/tex]

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the slope of the line perpendicular to the given line

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

we have

[tex]m1=-\frac{3}{4}[/tex] ------> slope of the given line

Find the value of m2

[tex]m2=-1/m1[/tex]

substitute

[tex]m2=-1/(-3/4)[/tex]

[tex]m2=\frac{4}{3}[/tex]

Step 3

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{4}{3}[/tex]

x-intercept is equal to [tex]6[/tex] --------> is the point [tex](6,0)[/tex]

substitute in the formula

[tex]y-0=\frac{4}{3}(x-6)[/tex]

[tex]y=\frac{4}{3}x-8[/tex]

therefore

the answer is the option

[tex]y=\frac{4}{3}x-8[/tex]

Sean Matthews' weekly earnings are subject to payroll taxes, including his tips. The deductions for social security and medicare are split between him and his employer. Understanding how these deductions work can enable him to maximize his total earnings.

The subject of the question pertains to Sean Matthews' earnings at the Duluxe Lounge, which involves payroll taxes on his wages and tips. From his regular wages of $300.00 for 40 hours, "payroll taxes" of 6.2% for Social Security and 1.45% for Medicare are deducted. The same deductions also apply to his reported tips of $500.00. These deductions are shared between Sean and his employer, though, it's possible that the employer's share might effectively be passed onto Sean in the form of lower wages.

Learning and understanding these financial procedures can significantly help individuals like Sean to maximise their total earnings.

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$736 will be his Net take home.

Net pay is the money you have left when your paycheck makes its way to you and all of the required taxes are taken out. To find Sean's net pay, both his earned wages and the reported tips will be considered for tax deductions.

Calculate total earnings for the week:
Wages = $300.00.
Total earnings = Wages + Tips = $300.00 + $500.00 = $800.00.

Assume a tax rate (federal, state, and other taxes) of 2%  
Tax deductions = $800.00 x 2% = $16.00.

Calculate net pay:
Net pay = Total earnings - Tax deductions = $800.00 - $16.00 = $736.00.

complete question:

Sean Matthews is a waiter at the Deluxe Lounge. In his first weekly pay in March, he earned $300.00 for the 40 hours he worked. In addition, he reports his tips for February to his employer ($500.00), and the employer withholds the appropriate taxes for the tips from this first pay in March.Calculate his net take-home pay assuming the employer withheld federal income tax (wage-bracket, married, 2 allowances), social security taxes, and state income tax (2%).

Answer:

the answer is 3

Step-by-step explanation:

just got it right on iready

To find the value of b in the equation 25s = 9b = 4c - s^2, we can substitute the given values and solve using the quadratic equation.

To find the value of b, we can use the given information and substitute the values of a, b, and c into the quadratic equation.

The equation is: c = 25s = 9b = 4c - s^2

Substituting the values:

25s = 9b = 4c - s^2

25s = 9b = 4c - s^2

Now we can solve for b:

9b = 4c - s^2

9b = 4(-0.0211) - (9)^2

9b = -0.0844 - 81

9b = -81.0844

b = -81.0844/9

b = -9.01

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Answer:

Heres the correct answer. Hope this helps anyone who needs it!!!

Step-by-step explanation:

The polynomial function is one that involves only non-negative number powers of x, unlike a polynomial, cubic, or quartic function, and further calculation can be defined as follows:

Given:

[tex]\bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

To find:

Solution:

[tex]\to \bold{f(x)=x^4-3x^3-23x^2+75x-50}[/tex]

Let [tex]\bold{x=2}[/tex]

[tex]\to \bold{f(2)=2^4-3(2)^3-23(2)^2+75(2)-50}\\\\\to \bold{f(2)=16-3(8)-23(4)+75(2)-50}\\\\\to \bold{f(2)=16-24-92+150-50}\\\\\to \bold{f(2)=166-166}\\\\\to \bold{f(2)=0}\\\\[/tex]

So the factor is [tex]\bold{(x-2)}[/tex].

[tex]\to \bold{(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]

Therefore, the final answer is "[tex]\bold{ f(x)=(x-5)(x-2)(x-1)(x+5)}\\\\[/tex]".

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The unit rate for 521 miles in 14 hours is 37.2 miles per hour

Given:

Total distance travelled = 521 miles

Total time taken = 14 hours

Unit rate = Total distance travelled ÷ Total time taken

= 521 miles ÷ 14 hours

= 37.214285714285

Approximately, 37.2 miles per hour

Therefore, unit rate for 521 miles in 14 hours is 37.2 miles per hour

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Answer: 9 hours

Step-by-step explanation:

Given proportion : [tex]\frac{\text{180 Kilometers}}{\text{3 hours}}=\frac{\text{540 Kilometers }}{x}[/tex]

To find the value of x , we need to multiply 3x hours and divide 180 Kilometers on both the sides, we get

[tex]\text{x}=3\times\frac{540}{180}\text{hours}\\\\\Rightarrow\ x=3\times3\\\\\Rightarrow\ x=9\text{ hours} [/tex]

Hence, the value of x = 9 hours.

Answer:

The value of a=6[/tex]

Step-by-step explanation:

step 1:-

col linearity of three points :-

We know that slopes of two parallel lines are equal.If two lines having the same slope pass through a common point ,then two lines will coincide . Hence ,If A,B,C are three points in the X Y- plane, then they will lie on a line,

that is three points are col linear if and only if Slope of AB= slope of BC

step 2:-

Since the given three points are col-linear, we have

Slope of AB= slope of BC

given points are A(2,-2) ,B(-6,2) and C(a,-4)

Step 3 :-

Slope of AB= slope of BC

[tex]\frac{2-(-2)}{-6-2} =\frac{-4-2}{a+6}[/tex]

[tex]\frac{-1}{2} =\frac{-6}{a+6}

 by cross multiplication

we get \\a+6=12\\

Step 4:-

The value of a=6[/tex]

Answer:

There are 14 $10 bills and 16 $20 bills.

Step-by-step explanation:

Let

x = number of $10 bills

y = number of $20 bills

The sum of the value of x and y is $460.

10 x + 20 y = 460   [1]

The sum of x and y is equal to the total number of bills.

x + y = 30

y = 30 - x   [2]

We replace [2] in [1],

10 x + 20 (30 - x) = 460

10 x + 600 - 20 x = 460

-10 x = -140

x = 14

We can get y if we replace this value of x in [2].

y = 30 - 14 = 16

The largest number which divides 149 and 101 , leaving remainder of 5 : 48

The division operation is one of the basic arithmetic operations

Common signs used are [tex] \large {\boxed {:}}} [/tex] or [tex] \large {\boxed {\slash}} [/tex]

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by:

[tex] \large {\boxed {\bold {divident:divisor=quotient+remainder}} [/tex]

example:

7: 3 = 2 + 1

Division operation statement:

"7 divided by 3 equals 2 remainder 1"

A number have many factors

A common factor is a factor of two / more numbers.

Greatest common factor (GCF or HCF = Highest Common Factor) is the largest of the common factors

The largest number which divides 149 and 101 leaving remainder of 5

Division operation:

We find the value of x which is the GCF of the numbers 144 and 96

149 - 5 = 144

101 - 5 = 96

We look for GCF from factors of 144 and 96

GCF of 144 and 96 is 48

Or we can use prime factors:

144: 2⁴ X 3²

96: 2⁵ X 3

GCF = 2⁴ X 3 = 48

Highest common factor

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Keywords : Greatest common factor , division, prime factors

The exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent,"

it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The given expression is 5x5x5x5x5x5. The exponent form of the number will be written below,

E = 5x5x5x5x5x5

E = 5⁶

Therefore, the exponent form of the given multiplication 5x5x5x5x5x5 is 5⁶.

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A paint drying situation, has the standard deviation 1.93. The detailed solution is given below.

Given :

Standard Deviation, [tex]\sigma = 7[/tex]

Mean, [tex]\mu = 75[/tex]

Sample, n = 25

Solution :

A) We know that,

[tex]z = \dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n} }}[/tex]     ---- (1)

Now put the values of [tex]\rm x,\;\mu,\;\sigma \;and \;n[/tex] in equation (1) we get,

[tex]z = \dfrac{72.3-75}{\dfrac{7}{\sqrt{25} }}[/tex]

z = -1.93

Therefore, 72.3 is 1.93 standard deviations below the mean.

B) From the above part we know that z = - 1.93.Therefore p-value is,

P(-1.93) = 0.03

Since [tex]\alpha[/tex] = 0.01 and p-value = 0.03, this means that the p-value is greater than the fail to reject the null hypothesis.

C) The p-value for [tex]z\leq -2.8[/tex]

is 0.00256

Therefore, the [tex]\alpha[/tex] for the test procedure that rejects the null hypothesis when [tex]z\leq -2.8[/tex] is 0.0026.

D) For alternate hypothesis,

[tex]\rm \beta (\mu') = P(X>\mu_0-z_1_-_\alpha \frac{\sigma}{\sqrt{n} }|\mu')[/tex]

[tex]\rm = P(-z_1_-_\alpha +\dfrac{\mu_0-\mu'}{\dfrac{\sigma}{\sqrt{n} }})[/tex]

For [tex]\alpha[/tex] = 0.0026

[tex]\rm \beta (70)=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{25} }})[/tex]

[tex]\rm \beta (70) = 1-P(-2.7949+3.5714)=1-P(0.7765)[/tex]

[tex]\beta (70)=1-0.78128\approx 0.2187[/tex]

E) Now we want n when

[tex]\beta (70) = 0.01[/tex]

[tex]\rm 0.01=1- P(-z_0_._9_9_7_4 +\dfrac{75-70}{\dfrac{7}{\sqrt{n} }})[/tex]

[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=0.99[/tex]

[tex]P(-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }})=P(2.3262)[/tex]

[tex]-2.7949+\dfrac{5}{\dfrac{7}{\sqrt{n} }}=2.3262[/tex]

[tex]\rm \sqrt{n} = 7.1695[/tex]

n = 51.4

Therefore we need n = 52.

F)

[tex]\rm p-value = P(\bar{X}\leq \bar{x})[/tex]

[tex]\rm p-value = P(\bar{X}\leq 72.3)=P(z\leq \dfrac{72.3-76}{\dfrac{7}{5}})[/tex]

[tex]\rm p-value = P(z\leq -2.643)[/tex]

[tex]\rm p-value = 0.00411[/tex]

Since p-value is larger that .01 therefore we fail to reject [tex]\mu[/tex] = 76.

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The inequality that represents the graph is y < x.

The inequality that represents the graph is y < x. This inequality represents the region below the line that forms the graph. In this case, the line starts at the origin and has a slope of 1, meaning that for every increase of 1 unit on the x-axis, the y-coordinate increases by 1 unit as well.

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Final answer:

The probability that an apartment is on the 2nd floor or has 2 bedrooms is 0.7727 or 77.27%.

Explanation:

To find the probability that an apartment is on the 2nd floor or has 2 bedrooms, we need to determine the total number of apartments that satisfy either of the conditions.

On the 2nd floor, there are 2 apartments with 1 bedroom, 2 apartments with 2 bedrooms, and 2 apartments with 3 bedrooms. This gives us a total of 2 + 2 + 2 = 6 apartments on the 2nd floor.

Out of the total distribution of apartments, there are 3 apartments with 1 bedroom, 4 apartments with 2 bedrooms, and 4 apartments with 3 bedrooms. This gives us a total of 3 + 4 + 4 = 11 apartments with 2 bedrooms.

The probability of an apartment being on the 2nd floor or having 2 bedrooms is given by:

Probability = (Number of apartments on the 2nd floor + Number of apartments with 2 bedrooms) / Total number of apartments

Probability = (6 + 11) / (6 + 1 + 1 + 2 + 2 + 2 + 1 + 2 + 4 + 1) = 17 / 22 = 0.7727 or 77.27%

First let us calculate for the z score using the formula:

z = (x – u) / s

where x = 8, u is the mean = 12.7 years, s is the standard deviation

z = (8 – 12.7) / 2.5

z = -1.88

From the standard probability tables, the p value at z = -1.88 is:

P = 0.0301 = 3.01%

Answer:

C

Step-by-step explanation:

k is the slope of the line

The equation of the line is y = kx. Therefore, the special thing about k is that it is the slope of the line.

Using a slope intercept equation,

y = kx + b

where

Therefore, the y-intercept of the line y = kx is zero.

What is special about k is that it is the slope of the line y = kx.

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Answer:

D) 8²

Step-by-step explanation:

Evaluate each of the choices and see which one is equal to 64.

_____

It helps if appropriate mathematical symbols are used.

Final answer:

There is a family of normal probability distributions, each representing different populations or sets of data with varying mean and standard deviation values.

Explanation:

Yes, there is a family of normal probability distributions. The normal distribution is a continuous probability distribution that can take on different forms depending on the mean and standard deviation. The family of normal distributions is characterized by different mean and standard deviation values, which result in different shapes of the distribution curve.

For example, the standard normal distribution has a mean of 0 and a standard deviation of 1, and its curve is symmetrical around the mean. Other normal distributions may have different means and standard deviations, resulting in curves that are shifted or stretched.

Each normal distribution in the family represents a different population or set of data, and knowing the specific mean and standard deviation allows us to calculate probabilities and make statistical inferences.