6.Write the answer in scientific notation.
(8.8 x 105) + (2.2 x 103)

Answer:

Q8 It is because the data collected are too scattered and cannot show an obvious trend.

if it's correct pls mark brainliest tks

Answer:

15 i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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The Taylor polynomials of degree 2 and 3 centered at 3 for the function \(f(x)=x^4-7x\) are:

\(T2(x) = 54 + 65(x-3) + 54(x-3)^2\\T3(x) = 54 + 65(x-3) + 54(x-3)^2 + 6(x-3)^3\)

The Taylor polynomials centered at 3 for the function \(f(x)=x^4-7x\) up to degree 3 are given by:

\(T2(x) = f(3) + f'(3)(x-3) + (f''(3)/2!)(x-3)^2\\T3(x) = T2(x) + (f'''(3)/3!)(x-3)^3\)

where f'(x), f''(x), and f'''(x) are the first, second, and third derivatives of f(x), respectively.

We first compute the derivatives of f(x):

\(f'(x) = 4x^3 - 7\\f''(x) = 12x^2\\f'''(x) = 24x\)

Next, we evaluate f(3) and its derivatives at x=3:

\(f(3) = 3^4 - 7(3) = 54\\f'(3) = 4(3)^3 - 7 = 65\\f''(3) = 12(3)^2 = 108\\f'''(3) = 24(3) = 72\)

Substituting these values into the formulas for T2(x) and T3(x), we get:

\(T2(x) = 54 + 65(x-3) + (108/2!)(x-3)^2 = 54 + 65(x-3) + 54(x-3)^2\\T3(x) = T2(x) + (72/3!)(x-3)^3 = 54 + 65(x-3) + 54(x-3)^2 + 6(x-3)^3\)

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Answer:

A ≈ 8.6 ft²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) × 7 × 3 × sin55°

  = \(\frac{1}{2}\) × 21 × sin55°

  = 10.5 × sin55°

  ≈ 8.6 ft²( to 1 dec. place )

1080 inches²  are the dimensions of the box with maximum volume .

What is rectangle?

rectangular box length = 24 inches

                       width = 45 inches

maximum volume = 24 * 45

                              = 1080 inches²

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a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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Answer:

-> Supplementary

-> Add up to 180°

Explanation:

       A straight line has a measurement of 180°. Supplementary angles are angles that, when added together, equal 180°.

       Since angles 5 and 6 make up a straight line, we know they will add up to 180°.

Answer:

y = -1/5x + 6.4

Step-by-step explanation:

Use the point-slope formula.

y-y₁ = m(x -x₁)

so...

y-7 = -1/5(x - (-3))

y = -1/5x+ 32/5

and you need you can change 32/5 to 6.4

Hope this helps!

a) Relative rate of change = 8/t

b) Relative rate of change at t = 1

c) Relative rate of change = -2t

d) Relative rate of change at t = -28

A more detailed explanation of the answer.

(a) To find the relative rate of change for the function f(t) = t⁸, we first need to find the derivative of f(t) with respect to t.

f'(t) = 8t⁷

The relative rate of change is the ratio of the derivative to the function itself, which is:

Relative rate of change = f'(t) / f(t) = (8t⁷) / (t⁸) = 8/t

(b) To evaluate the relative rate of change at t = 3, we simply substitute t = 3 into the relative rate of change expression:

Relative rate of change at t = 3 = 8/3

To evaluate the relative rate of change at t = 8, we substitute t = 8:

Relative rate of change at t = 8 = 8/8 = 1

Now, consider the function f(t) = e power (-t²).

(a) To find the relative rate of change, we first need to find the derivative of f(t) with respect to t.

f'(t) = -2te power (-t²)

The relative rate of change is the ratio of the derivative to the function itself:

Relative rate of change = f'(t) / f(t) = (-2te power (-t²)) / (e power (-t²)) = -2t

(b) To evaluate the relative rate of change at t = 14, we substitute t = 14 into the relative rate of change expression:

Relative rate of change at t = 14 = -2(14) = -28

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Answer:

1. (-94)

2. (+3)

Step-by-step explanation:

Hope this helps!!

Step-by-step explanation:

As you can see in first expression both have " - " sign infront of them....so all uh need to do is put that minus sign there and add expression cuz ( - ) and ( - ) will be ( + )

= - 94

In second expression the question

- 1 - ( - 4 )

As we know ( - ) × ( - ) will be ( + ) as it is multiplied so we need to change the sign

- 1 + 4 .............[ ( - ) and ( + ) = ( - ) ] so we need to subtract but the plus sign here has greater number so the sign will be plus ....

= + 3

\(...\)

In a survey of adults who set themselves some fitness targets, 5% achieved all of them, and 15% achieved some of them. Another fitness survey questions 400 adults. There are 80 people who expect to achieve all of their targets.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Given that:

5% achieve all of them

15% achieve some of them

Total percentage = 5% + 15%

                              = 20%

there are 400 adults = 400× 20%

                                    = 80% target

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Answer:

see below

Step-by-step explanation:

The circumference is the distance around a circle, think of it as a ribbon

The area is the amount to cover, like a round table cloth

The area of a circle represents the total amount of content inside the circle.

The circumference of a circle is the same as the perimeter, which is the total amount of length outside the entire circle.

Both are also found different using different formulas.

Best of Luck!

Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer: 3750

Step-by-step explanation:

Answer:

1) we get value of  x = -4 and y = -4

2) we get value of x = -7 and y = 3

Step-by-step explanation:

1) Identify the solution to the system of equations.

\(y=\frac{3}{2}x+2\:and\:y=\frac{1}{4}x-3\)

Looking at the graph we can see that two points intersect at (-4,-4) so it is the solution of the system of equations. Verifying by solving:

Let:

\(y=\frac{3}{2}x+2--eq(1)\\y=\frac{1}{4}x-3--eq(2)\)

Put value of y from eq(1) into eq(2)

\(\frac{1}{4}x-3=\frac{3}{2}x+2\\\frac{x-12}{4}=\frac{3x+4}{2} \\2(x-12)=4(3x+4)\\2x-24=12x+16\\2x-12x=16+24\\-10x=40\\x=40/-10\\x=-4\)

Now put value of x in eq(2)

\(y=\frac{1}{4}x-3\\y=\frac{1}{4}(-4)-3\\y=-1-3\\y=-4\)

So, we get x = -4 and y = -4

2)

\(9x+14y=-21\\-x+7y=28\)

Let: \(9x+14y=-21--eq(1)\\-x+7y=28--eq(2)\)

Multiply eq(2) with 9 and add both equations

\(9x+14y=-21\\-9x+63y=252\\------\\77y=231\\y=231/77\\y=3\)

Put value of y in eq(2)

\(-x+7y=28\\-x+7(3)=28\\-x+21=28\\-x=28-21\\-x=7\\x=-7\)

So, value of x = -7 and y = 3

Answer:

$15.80

Step-by-step explanation:

20% × 79 = 15.8

To graph the function \(y=2x^2\), use technology such as graphing software to plot the points and visualize the parabolic curve.

Determine a range of x-values that you want to plot in the quadratic function graph. Let's choose the range from -5 to 5 for this example.

Substitute each x-value from the chosen range into the function \(y=2x^2\) to find the corresponding y-values. Here are the calculations for each x-value:

For x = -5:

y = \(2(-5)^2\) = 2(25) = 50

So, the first point is (-5, 50).

For x = -4:

y = \(2(-4)^2\) = 2(16) = 32

So, the second point is (-4, 32).

For x = -3:

y = \(2(-3)^2\) = 2(9) = 18

So, the third point is (-3, 18).

Continue this process for x = -2, -1, 0, 1, 2, 3, 4, and 5 to find their respective y-values.

Plot the points obtained from the previous step on a coordinate plane. The points are: (-5, 50), (-4, 32), (-3, 18), (-2, 8), (-1, 2), (0, 0), (1, 2), (2, 8), (3, 18), (4, 32), and (5, 50).

Connect the plotted points with a smooth curve. Since the function \(y=2x^2\) represents a parabola that opens upward, the curve will have a U-shape.

Label the axes as "x" and "y" and add any necessary scaling or units to the graph.

By following these steps, you can find the points and graph the function \(y=2x^2\).

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Answer::

Explanation:

Given the general cosine function:

We want to determine the function that has the following properties:

• Amplitude = 2

• Period = 4π

Using the period formula given above:

From the given options, the function that satisfies the required property is:

The answers to all parts are shown below.

1. The number of ways are

= 11!/ (11-1)!

= 11! /10!

= 11

2. The favorable outcomes of the event

Triangle= 1

star = 4

Not square= 9

Not circle= 8

3. C( 12, 1)= 12!/ 1! 11!

= 12 ways

4. Choose a cat = C(18, 12)= 18! / 12! 6!

= 18564

5. Choose a dog

= C(18, 6)

= 18!/ 6! 12!

= 18564

6. Bus arrive on time= 1-2/7 = 5/7

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Answer:To find the probability of the student taking English, History I, Algebra, and Spanish II in the first semester, and History II, Spanish III, Geometry, and Biology in the next semester, we need to calculate the probability of each event occurring and then multiply them together.

First Semester:

The student needs to choose 4 classes out of the 17 classes offered. So, the probability of choosing English, History I, Algebra, and Spanish II is:

P(English) * P(History I) * P(Algebra) * P(Spanish II) = 1/17 * 1/16 * 1/15 * 1/14

Second Semester:

Similarly, the student needs to choose 4 classes out of the remaining 13 classes offered (since one class has already been taken). So, the probability of choosing History II, Spanish III, Geometry, and Biology is:

P(History II) * P(Spanish III) * P(Geometry) * P(Biology) = 1/13 * 1/12 * 1/11 * 1/10

To find the overall probability, we multiply the probabilities from both semesters together:

P = (1/17 * 1/16 * 1/15 * 1/14) * (1/13 * 1/12 * 1/11 * 1/10)

Calculating this expression gives us the probability of the student following the specified schedule.

Step-by-step explanation:

By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

(x + 4)²

= x2 + 16 + 8x

By graphing a plot point using the x-intercept form, the function (x + 4)2 is shown to be x2 + 16 + 8x.

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Step-by-step explanation:

15: bottom left = 360 = full freshman class

180 play a sport -- of those, 112 are NOT on the honor roll, meaning that 112 are only in a school sport. thus,

middle right = 112

180 - 112 = students that play a sport that are not not on the honor roll = students that play a sport and are on the honor roll = 68

middle center = 68

216 - 68 = students that are on the honor roll and are not in both honor roll and a sport = students that are on the honor roll and not in a sport = 148

middle left = 148

16. P(school sport | honor roll) = probability a student is on a school sport GIVEN that they are on the honor roll = P(A and B)/P(B) = 68/148 =  45.9%

a) Use α = 0.02.The hypothesis can be set up as: H0: p1 - p2 = 0 and H1: p1 - p2 ≠ 0,where p1 is the proportion of nurses poked by a needle in hospital with a standard safety protocol and p2

The z-score can be calculated as\(:$$z = \frac{0.186-0.25}{0.094} = -0.682$$\)The critical z-value at α = 0.02 can be obtained from the standard normal distribution table, which is ± 2.33.Therefore, since the calculated z-value (-0.682) does not exceed the critical value (-2.33 and 2.33), we can conclude that there is not a significant difference in the proportions of nurses poked by a needle in hospitals with a standard safety protocol and a new protocol.

b) Calculate and interpret the related confidence interval. The confidence interval can be calculated as\(:$$\hat{p}_1 - \hat{p}_2 ± z_{0.01}\sqrt{\hat{p}_1(1-\hat{p}_1)\frac{1}{n_1} + \hat{p}_2(1-\hat{p}_2)\frac{1}{n_2}}$$where $z_{0.01}$ is the critical z-value at 99% confidence level. The confidence interval can be given as:$$0.186 - 0.25 ± 2.33\sqrt{0.186(1-0.186)\frac{1}{43} + 0.25(1-0.25)\frac{1}{48}} = (-0.191, 0.051)$$\)Since the confidence interval includes zero, we can conclude that the difference in proportions of nurses poked by a needle in hospitals with a standard safety protocol and a new protocol is not statistically significant at the 99% confidence level.

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The volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis is 160π/3 cubic units.

To use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis, we need to integrate the volume of a cylindrical shell.

The formula for the volume of a cylindrical shell is:

V = 2πrhΔx

where:

r is the distance from the axis of rotation (the x-axis) to the edge of the shell

h is the height of the shell (which is equal to the difference between the y-coordinates of the two curves)

Δx is the thickness of the shell (which becomes an infinitesimal dx in the limit)

We can see from the given equations that the two curves intersect at x=0, so we will integrate from x=0 to x=a, where a is the point where the curve y=2 intersects the x-axis. To find a, we set y=2 and solve for x:

y = |x|/4 = 2

|x| = 8

x = ±8

Since we are only interested in the region bounded by the curves in the first quadrant, we take a=8.

Now we can set up the integral for the volume using the shell method:

V = ∫(0 to 8) 2πr * h * dx

= ∫(0 to 8) 2πx * [2 - (|x|/4)] * dx

Note that we multiply by 2 because we are integrating only over the first quadrant, and we obtain the full volume by doubling that result.

Since the function inside the integral is not continuous at x=0, we split the integral into two parts:

V = 2 ∫(0 to 8) 2πx * [2 - (x/4)] * dx + 2 ∫(0 to 8) 2πx * [2 - (-x/4)] * dx

Simplifying, we get:

V = 2π ∫(0 to 8) (15/2)x - (1/4)x^2 dx

= 2π [(15/4)x^2 - (1/12)x^3] | from 0 to 8

= 160π/3

Therefore, the volume of the solid generated by revolving the regions bounded by the curves and lines about the x-axis is 160π/3 cubic units.

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