A cake has 65 slices.

Harry ate 1 slices; Jack ate 19 slices; Dave ate 40 & Mary ate 4 slices.

What fraction of the cake is remaining?

By using the coordinates of the labeled point, the point-slope equation of the line include the following: D. y + 5 = -3(x - 3)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

0 5 2 -2

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 5)/(0 - 3)

Slope (m) = -9/3

Slope (m) = -3

At data point (3, -5) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 3(x - 3)  

y + 5 = -3(x - 3)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

a) Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539

b) \(t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5\)    

The degrees of freedom are given by:

\(df=n-1=49-1=48\)  

The p value is given by:

\(p_v =P(t_{(48)}<-1.5)=0.07\)  

c) \(7359-2.01\frac{840}{\sqrt{49}}=7117.8\)    

\(7359+2.01\frac{840}{\sqrt{49}}=7600.2\)    

d) For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval

Step-by-step explanation:

Part a and b

Data given

\(\bar X=7359\) represent the sample mean

\(\sigma=840\) represent the population standard deviation

\(n=49\) sample size  

\(\mu_o =7539\) represent the value to test

t would represent the statistic  

\(p_v\) represent the p value

Hypothesis to verify

We want to verify if the mean life is different from 7539 hours, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 7539\)  

Alternative hypothesis:\(\mu < 7539\)  

The statistic for this case would be given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info given we got:

\(t=\frac{7359-7539}{\frac{840}{\sqrt{49}}}=-1.5\)    

The degrees of freedom are given by:

\(df=n-1=49-1=48\)  

The p value is given by:

\(p_v =P(t_{(48)}<-1.5)=0.07\)  

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 7539

Part c

The confidence interval for the mean is given by the following formula:

\(\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}\)   (1)

We can find the critical value using the confidence level given of 95% and using the t distribution with 48 degrees of freedom we got \(t_{\alpha/2}=\pm 2.01\)

Now we have everything in order to replace into formula (1):

\(7359-2.01\frac{840}{\sqrt{49}}=7117.8\)    

\(7359+2.01\frac{840}{\sqrt{49}}=7600.2\)    

Part d

For this case since the confidence interval contains the value of 7539 we don't have enough evidence to reject the null hypothesis at the significance level given of 5%. same conclusion using the hypothesis test and with the confidence interval

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

Step-by-step explanation

· It costs about $2.34 per square foot on average to hang sheetrock on the ceiling, with a range of approximately $2.07 to $2.61 per square foot. Expect to pay between $500 and $700 to hang and finish sheetrock on the ceiling. However, the overall cost depends on the room’s size, height, and finish options.

Answer:

5,300 YAN po yong answer ma'am #CARRY ON LEARNING

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:

the value of x is between -4 and 4

If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.

A real number is any number that can be expressed as a decimal or fraction and exists on the number line.

If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.

Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.

From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.

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Regular pay rate x 40 hours = Regular pay, plus

Regular pay rate x 1.5 x 2 hours = Overtime pay, equals

He works 47 hours and his pay rate is 17.00

His gross pay will be:

40*17 = $680

Now, his gross pay plus overtime will be:

$680 + (1.5*7*17) = $680 + $178.5 = $858.5

-----------------------------------------------------------------------------

Mark worked 51 hours and his pay rate is $15.00

Gross pay before overtime = 40*15 = $600

Gross pay plus overtime = $600 + 11*1.5*15 = $847.5

Answer:

OPTION D

2^³/5

= 5√2^3

Option D is legit.

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

0.16

Step-by-step explanation:

The computation of the minimum no of usual smokers expected to get out of 20 adults is shown below:

Here the standard deviation is

\(= \sqrt{npq} \\\\= \sqrt{20\times 0.18 \times (1 - 0.18)}\\\\= \sqrt{20\times 0.18\times 0.82}\\\\= \sqrt{2.952}\)

= 1.72

Now the minimum no of smokers is

\(= np - 2\times 1.72\\= 20 \times 0.18 - 3.44\\\\= 0.16\)

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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With compound interest of 6% paid semiannually, a deposit of $900 would result in $1,191.02 after 5 years, while simple interest would earn $270, resulting in a total of $1,170.

To calculate the future value of an investment with compound interest, we can use the following formula:

FV =\(PV * (1 + r/n)^{(n*t)}\)

where FV, PV, r, n and t is the future value, present value, annual interest rate, number of compounding periods per year and number of years respectively.

In this case, the present value (PV) is $900, the annual interest rate (r) is 6%, and the interest is compounded semiannually, so there are 2 compounding periods per year (n=2). The period (t) of investment  is 5 years.

Using these values, we can calculate the future value (FV) as follows:

FV = \(\$900 * (1 + 0.06/2)^{(2*5)\)

= \(\$900 * (1.03)^{10\)

= $1,191.02

Therefore, the future value of the investment after 5 years with compound interest would be $1,191.02.

If the interest were simple interest instead of compound interest, the calculation would be simpler. Simple interest is calculated as follows:

I = P x r x t

where I is the interest, P is the principal or present value, r is the interest rate, and t is the time period.

In this case, the interest rate is still 6% and the investment period is still 5 years, but the interest is calculated only on the principal amount of $900. Therefore, the interest earned would be:

I = $900 x 0.06 x 5

= $270

Therefore, the total amount after 5 years with simple interest would be the sum of the principal and the interest earned, which is:

Total = $900 + $270

= $1,170

Therefore, if the interest were simple interest instead of compound interest, the total amount after 5 years would be $1,170, and the interest earned would be $270.

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Answer: 2 9/20

Step-by-step explanation:

First, rewriting our equation with parts separated

=6+14−3−45

Solving the whole number parts

6−3=3

Solving the fraction parts

14−45=?

Find the LCD of 1/4 and 4/5 and rewrite to solve with the equivalent fractions.

LCD = 20

520−1620=−1120

Combining the whole and fraction parts

3−1120=2920

Solution by Formulas

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

254−195

Applying the fractions formula for subtraction,

=(25×5)−(19×4)4×5

=125−7620

=4920

Simplifying 49/20, the answer is

=2 9/20

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.

given

The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.

Calculating the sample proportion is necessary:

The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:

P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031

Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:

\(z = (0.476 - 0.34) / 0.031 = 4.39\)

The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.

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Answer:

x = 59/4

Step-by-step explanation:

4x + 9 = 68

Subtract 9 from both sides.

4x + 9 - 9 = 68 - 9

4x = 59

Divide both sides by 4.

4x/4 = 59/4

x = 59/4

Answer:

X=0.75

Step-by-step explanation:

Step 1:

68-9=59

Step 2:

59 divided by 4= 14.75

Step 3:

0.75=3/4

14 3/4=14.75

Solution:

X=0.75

Another way is 59/4=14.75

The graph of the linear equation, x = 6, is shown in the image attached below.

The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.

Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.

Thus, the graph of the linear equation, x = 6, is shown in the image attached below.

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Answer:

If the outside diameter of the wheel is 66cm, it will travel 1 wheel circumference. Circumference is Pi x diameter = 3.14 x 66 = 207.24 cm.Step-by-step

Explanation:

If the diameter is of the wheel (without the tire) you need to calculate the actual diameter from the outermost edge of the tire.

its 9/7 as a mixed number

hope this helps !

Answer:

hi

Step-by-step explanation:

Answer:

2(10 + y)

Step-by-step explanation:

There are more like this 6(5 + y)

30 + y

Hope you got it.

Answer:

9.8

Step-by-step explanation:

updated

9^2=x^2+4^2

9*9=x*x+4*4

81=x*x-16

+16. +16

97=x*x

√97=√x*x

√97=x

So the answer is √97, but the question wants it rounded so it's actually 9.8

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Answer:

To graph the equation y = 1/2x - 4, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

In this equation, the slope is 1/2, and the y-intercept is -4. The slope represents the steepness of the line, and the y-intercept is the point at which the line crosses the y-axis.

To graph the equation:

Plot the y-intercept, which is (-0, -4)

Using the slope, we can pick a second point on the line. The slope of 1/2 tells us that for every 2 units in the x direction, we will move 1 unit in the y direction. So we can pick a point that is 2 units to the right of the y-intercept, such as (2,0).

Connect the two points to get a straight line

The resulting graph will be a straight line that passes through the point (-0, -4) and (2, 0) and continues in both directions.

Alternatively, you can use a table of values to plot the points that belongs to the line and connect them, for example:

x | y

-2 | -5

-1 | -4.5

0 | -4

1 | -3.5

2 | -3

These are few points on the graph and with more points you can connect them and see the shape of the graph.

Step-by-step explanation:

Answer:

It should be 42.4

Answer:

sin(x)

Step-by-step explanation:

sec x tanx(1 - sin^2 x)

1 - sin^2 x = cos^2 x

sec(x)tan(x)cos^2(x)

\(\frac{1}{cos(x)}\) * \(\frac{sin(x)}{cos(x)}\) * cos^2(x)

\(\frac{sin(x)cos^2(x)}{cos^2(x)}\)

sin(x)

Step-by-step explanation:

A rectangular prism has a length, width, and height of 2/3 inch, 3/5 inch, and 4/7 inch, respectively.

The volume of the rectangular prism is

24/105

cubic inch.

The quadratic function is given by the following expression:

The direction at which the graph opens is determined by the signal of the number multiplying x². If the number is positive then the graph opens upwards, if it is negative it opens downward. In this case it is negative so it opens donward.

The vertex of a quadratic expression can be found by the following expression:

Where a is the number multiplying "x²", while b is the number multiplying "x". Applying the data from the problem we have:

To find the value of "y" for the vertex we need to apply the coordinate for x on the expression. We have:

The coordinates of the vertex are (-1,4).

To sketch a graph we need to find the x-intercept and y-intercept of the function. These are given when f(x) = 0 and x=0 respectively. Let's find these points.

The x intercept happens in two points -3 and 1, while the y intercept happens in the point 3. With this and the vertex we can sketch the function.