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He rented the pressure washer for 4 hours, given that the total bill was $86.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = total number of hours he rented the pressure washer

The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.

Hence, the equation will be 50 + 9x = 86.

Solve for x.

50 + 9x = 86

9x = 86 - 50

9x = 36

x = 4

total number of hours he rented the pressure washer = 4

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer: 40 . 2 and 40 + 40

Step-by-step explanation:

The expression which shows the saving is 40 + 40 and 40 x 2. The correct options are C and D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the amount of money saved by Erica is $40. The expression which represents the savings will be,

40 + 40 = 80

40 x 2 = 80

Therefore, the expression which shows the saving is 40 + 40 and 40 x 2. The correct options are C and D.

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Answer:

All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.

want to come up down to gotta amen Cheech jjk

Using the theories of Application of derivative,we got that  59.11221inches³/sec  is rate of volume changing when the radius is 2.3 inches.

We are given rate of change of radius (dr/dt)=0.6inches

We know very well that volume of sphere is given by (4/3)πr³

where r is the radius of the sphere.

Now, differentiating the volume with respect to radius, we get

=>dV/dr=4πr²

=>dV/dt=(dv/dr)·(dr/dt)

=>dV/dt=4πr².(dr/dt)

We are given that dr/dt=0.6inches/sec

So, dV/dt=4πr²·(0.6)

Now, putting values of r=2.3

 dV/dt=4π(2.3)²×(0.6)

=>dV/dt=4×3.14×2.3×2.3×0.6

=>dV/dt=59.11221inches³/sec

Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.

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The Mean for the following numbers: -5, 21, 14, 2, 48, and Level of difficulty = 1 of 2 is 16.

The mean is the average of a set of numbers. It is calculated by adding all the numbers in the set and then dividing the sum by the total number of numbers in the set. In this case, we have the following numbers: -5, 21, 14, 2, 48.

To find the mean, we need to add all the numbers together and then divide by the total number of numbers. So, the sum of these numbers is: -5 + 21 + 14 + 2 + 48 = 80

To find the total number of numbers, we count them: 5

Therefore, the mean is: 80 / 5 = 16

Therefore, the mean of the given set of numbers is 16, rounded to two decimal places.

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Answer:

f(1) = 11

Step-by-step explanation:

f(x) = 3x + 8

Let x=1

f(1) = 3(1) +8

    = 3+8

   = 11

Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

Binomial distribution.

For the distribution to be applicable, the experiment must

1. Have a know and constant number of trials

2. Probability of success of each trial remains constant (and known if available)

3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

p = probability of success of each trial  = 1 / 6

x = number of successes  (0 ≤ x ≤ n)  = 5

C(n,x) = number of combinations of picking x identical objects out of n

Applying binomial distribution

P(x,n) = probability of x successes in an experiment of n trials.

= C(n,x) * p^x * (1-p)^(n-x)

For n = 25 trials with probability of success (roll a 6) = 1/6

and x = 5,6,7,8,...25

It is easier to calculate the complement by

P(5+ 6's) = 1 - P(<5 6's)

= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

= 1 - 0.59373

= 0.40626

= 0.4063 (to 4th decimal place)

Answer:

7/8 ≈ .9

y = -3x/4 + 4.75

x = 9 ⅓

Rotation

Step-by-step explanation:

1.) 7/8 = 0.875 The hundredths place is 7, which means we round up to 0.9

2.) Isolate the y on the left. Then divide both sides by 4

3.) Subtract 7 from both sides, then divide both sides by 3

Rotation turns around a point Reflection flips across a line.

Answer:

(0.30, 0.42)

Step-by-step explanation:

i took the test :)

this is because 1lb is equal to 0.0625oz

The car's speed after the given amout of time is 19.8 m/s²

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration. A point or object going straight ahead is accelerated when it accelerates or decelerates. Any alteration in an object's velocity could take the form of a change in direction of motion or a speed increase or reduction. The moon orbiting the earth, an apple falling to the ground, and a car stopped at a stop sign are a few instances of acceleration.

Average Acceleration =Change in Velocity/ Time Taken

So Change in Velocity is 10-x m/s

Time taken is 7.25 s

Given accelaration 4.11 m/s²

Putting the values we get,

4.11 = (10-x)/7.25

⇒29.8 = 10-x

⇒x=19.8 m/s²

​

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Answer:

EFG is 123°

Step-by-step explanation:

The given points (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

A point lies on a line if and only if it can be written as the sum of a scalar multiple of a direction vector and a position vector of the line.

To determine if each point lies on the line defined by X = -5 + t, y = 6t, and z = 6+ t, we can substitute each point into this equation to see if it is equivalent.

(a) (0, 30, 11):

-5 + t = 0, so t = 5

y = 6t = 6 × 5 = 30

z = 6 + t = 6 + 5 = 11

So, (0, 30, 11) can be written as -5 + 5i + 6 × 5j + 6k = -5i + 30j + 11k, which lies on the line.

(b) (5, 6, 11):

-5 + t = 5, so t = 10

y = 6t = 6 × 10 = 60

z = 6 + t = 6 + 10 = 16

So, (5, 6, 11) does NOT lie on the line.

(c) (-7, -12, 4):

-5 + t = -7, so t = -2

y = 6t = 6 × -2 = -12

z = 6 + t = 6 + -2 = 4

So, (-7, -12, 4) can be composed as -5 - 2i + -12j + 4k = -7i - 12j + 4k, which lies on the line.

Therefore, (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

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--The given question is incomplete; the complete question is

"Determine whether each point lies on the line.

X = -5 + t, y = 6t, z = 6+ t                                                                                                          (a) (0, 30, 11)                                                                                                                                (b) (5, 6, 11)                                                                                                                                          (c) (-7, -12, 4)"--

The answer is \(0.5544135^{\circ}$\)

given data

\({mean}(\mu)=185^{}$ \\Variance $\left(\sigma^{2}\right)=244$\)

\(\begin{aligned}&\sigma=\sqrt{244} \\&\sigma=15.6205\end{aligned}\)

\(\frac{P(x < 184)}{p(x < 203)}\)

\(\Rightarrow \frac{p\left(\frac{x-\mu}{\sigma} < \frac{184-185}{15.6205}\right)}{P\left(\frac{x-\mu}{\sigma} < \frac{203-185}{15.6205}\right)}\)

\(\Rightarrow \frac{P(z < -0.064)}{P(z < 1,1523)}\) (From z table)

\($\Rightarrow \frac{p(z < -0.06)}{p(z < 1.15)}$\)

\($\Rightarrow \quad \frac{0.47608}{0.87493}$\)

\($\Rightarrow 0.5544135^{\circ}$\)

\(=0.5544135^{\circ}$\)

What is analogue signal ?

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The experimental research provides higher control and allows for stronger causal inferences, while quasi-experimental research is more suitable when random assignment is not feasible.

Experimental and quasi-experimental research are two approaches used in scientific studies, but they differ in terms of their design and the level of control over variables.

⇒ Experimental research involves the manipulation of an independent variable to observe its effects on a dependent variable, while controlling for potential confounding variables. It assigns random assignment of participants to different conditions, allowing for causal inferences.

The researcher has control over the variables and can establish cause-and-effect relationships.

⇒ On the other hand, quasi-experimental research lacks random assignment of participants. Instead, pre-existing groups or naturally occurring variations are used. The researcher still manipulates the independent variable but cannot randomly assign participants. This limits the ability to establish strong causal relationships.

⇒ Quasi-experimental designs are used when random assignment is not possible. They are useful for studying phenomena in real-world settings, but caution must be exercised in drawing definitive causal conclusions.

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The main difference between experimental and quasi-experimental research is that experimental research involves random assignment and control groups, while quasi-experimental research lacks random assignment and control groups.

Experimental and quasi-experimental research are two common research designs used in social sciences and other fields. They differ in terms of random assignment, control groups, and the establishment of causality.

Experimental Research:

quasi-experimental research:

Overall, experimental research provides stronger evidence for cause-and-effect relationships, while quasi-experimental research is used when random assignment is not possible or practical.

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i. The Fourier transform of (t - 2) - 38(t - 3) is [(jw)^2 + 38jw]e^(-2jw). ii. The Fourier transform of e^(-2t)u(t) is 1/(jw + 2). iii. The Fourier transform of e^(-3t+12)u(t-4) can be obtained using the result of ii. as e^(-2t)u(t-4)e^(12jw). iv. The Fourier transform of e^(-2|t|)cos(t) is [(2jw)/(w^2+4)].

i. To find the Fourier transform of (t - 2) - 38(t - 3), we can use the linearity property of the Fourier transform. The Fourier transform of (t - 2) can be found using the time-shifting property, and the Fourier transform of -38(t - 3) can be found by scaling and using the frequency-shifting property. Adding the two transforms together gives [(jw)^2 + 38jw]e^(-2jw).

ii. The function e^(-2t)u(t) is the product of the exponential function e^(-2t) and the unit step function u(t). The Fourier transform of e^(-2t) can be found using the time-shifting property as 1/(jw + 2). The Fourier transform of u(t) is 1/(jw), resulting in the Fourier transform of e^(-2t)u(t) as 1/(jw + 2).

iii. The function e^(-3t+12)u(t-4) can be rewritten as e^(-2t)u(t-4)e^(12jw) using the time-shifting property. From the result of ii., we know the Fourier transform of e^(-2t)u(t-4) is 1/(jw + 2). Multiplying this by e^(12jw) gives the Fourier transform of e^(-3t+12)u(t-4) as e^(-2t)u(t-4)e^(12jw).

iv. To find the Fourier transform of e^(-2|t|)cos(t), we can use the definition of the Fourier transform and apply the properties of the Fourier transform. By splitting the function into even and odd parts, we find that the Fourier transform is [(2jw)/(w^2+4)].

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Answer:

Step-by-step explanation:

7x-11=4x+4(being vertically opposite abgles)

7x-4x=4+11

3x=15

x=15/3

x=5

angle 2+angle1=180 degree(being straight line)

7x-11+angle 1=180

7*5-11+angle 1=180

35-11+angle1=180

24+angle 1=180

angle 1=180-24

angle 1=156 degree

Answer:

15/17

Step-by-step explanation:

Remember SOH- CAH - TOA

(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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Answer:

7/n would be a algebraic express

Step-by-step explanation:

Answer:

Just do 8.4 times 7

Step-by-step explanation:

8.4 times 7 = 58.8

Answer:

$31.92

Step-by-step explanation:

28.50 x .12 = 3.42

3.42 + 28.50 = $31.92

The total cost is thirty-one dollars and ninety-two cents, which includes a tip of three dollars and forty-two cents. Here’s one way to find these amounts.

Let’s set up a proportion. We can substitute the amounts we know into the proportion.  

Now, we cross multiply. Amount of tip times one hundred equals twenty-eight dollars and fifty cents times twelve.  

Then, we divide both sides of the equation by one hundred. The total cost is the food cost plus the amount of the tip. So, the total cost of the meal is thirty-one dollars and ninety-two cents.

The system of equations to describe the condition is,

22x + 74y = 10274

48x +  61y = 10261

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Yesterday, the organization sold 22 regular tickets and 74 VIP tickets, raising $10,274

Today, 48 regular tickets and 61 VIP tickets were sold, bringing in a total of $10,261

Cost of regular ticket = ?

Cost of VIP ticket = ?

Suppose,

Cost of regular and VIP ticket are respectively,  x & y

22x + 74y = 10274

48x +  61y = 10261

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The critical value of 2.576. If |z| > 2.576, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To test the manufacturer's claim at a 1% significance level, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The medicine is 90% effective in relieving backache.

H₀: p = 0.9

Alternative hypothesis (H₁): The medicine is not 90% effective in relieving backache.

H₁: p ≠ 0.9

Where p represents the true proportion of people who experience relief from backache after taking the medicine.

To conduct the hypothesis test, we will use the sample proportion and perform a z-test.

Calculate the sample proportion:

p = x/n

where x is the number of people who experienced relief (160) and n is the sample size (200).

p= 160/200 = 0.8

Calculate the standard error:

SE = √(p(1 - p)/n)

SE = √((0.8 * (1 - 0.8))/200)

Calculate the test statistic (z-score):

z = (p - p₀) / SE

where p₀ is the hypothesized proportion (0.9 in this case).

z = (0.8 - 0.9) / SE

Determine the critical value for a two-tailed test at a 1% significance level.

Since we have a two-tailed test at a 1% significance level, the critical value will be z* = ±2.576 (obtained from a standard normal distribution table or calculator).

Compare the absolute value of the test statistic to the critical value to make a decision:

If the absolute value of the test statistic is greater than the critical value (|z| > z*), we reject the null hypothesis.

If the absolute value of the test statistic is less than or equal to the critical value (|z| ≤ z*), we fail to reject the null hypothesis.

Substituting the values into the equation, we can determine the test statistic and compare it to the critical value.

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Step-by-step explanation:

74 lakh 55 thousand 2 hundred 48