I need help with this question someone please help and explain. Find the sum of the first twenty-seven terms of an arithmetic series whose first term is -8 and the sum of the first seven-term is 28.

Answer:

18.25

Step-by-step explanation:

365 ÷ 20 = 18.25

Jon drove 365 miles on 20 gallons of gas, so to find out how many miles he got per gallon, you divide 365 miles by 20 gallons. The result is 18.25 miles per gallon.

To solve this problem, you need to divide the total number of miles that Jon drove by the number of gallons of gas he used. This is because the miles per gallon is calculated by dividing the total miles driven by the amount of gas used.

So, in this case, you would do the following calculation: 365 miles ÷ 20 gallons = 18.25 miles per gallon

This means that Jon got 18.25 miles per gallon of gas.

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For this case we have by definition, that the perimeter of the figure will be given by the sum of its sides, that is:

[tex]n + 3 + 6.3 + 4.5 = 18.6[/tex]

We add similar terms:

[tex]n + 13.8 = 18.6\\n = 18.6-13.8\\n = 4.8[/tex]

Thus, the correct option is option b. That is, [tex]4.8 \ in[/tex]

Answer:

[tex]4.8 \ in[/tex]

Answer: second option.

Step-by-step explanation:

The perimeter of the figure is the sum the lenghts of its sides.

You know that the perimeter of this figure is 18.6 inches.

You can observe that it has four sides and three lenghts are given.

Then, you can write this expression:

[tex]18.6in=3in+6.3in+4.5in+n[/tex]

Now you need to solve for "n" to calculate its value.

This is:

[tex]n=3in+6.3in+4.5in-18.6in[/tex]

[tex]n=18.6in-3in-6.3in-4.5in[/tex]

[tex]n=18.6in-13.8in[/tex]

[tex]n=4.8in[/tex]

Answer:x=100

Step-by-step explanation:

Since you know that g(x)=3x-11 all you have to do is substitute that into g(x)=289. So you get 3x-11=289. To get x you have to add 11 on both sides.

3x-11=289

+11 +11

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

3x = 300

Divide 3 on both sides to get x by itself

3x =300

---- -------

3 3

x=100

Answer: 6205 Hours

Explanation: The number of hours slept each night is 7

The total hours in one day is 24

the number of awake hours in one day would mean 24-7 which is equal to 17 hours

your awake 17 hours in a day

the number of days in a year is 365

to get the total number of hours your awake in a year, you’d do 17 x 365

Answer:

First multiple 7hours x 365 days in a year = 2555.

There are 24 hours in day. You want to sleep, for 7 hours.

Next, subtract 24 hours- 7 hours= 17 hours.

Finally, multiple 17 awake hours x 365=7254 hours.

Step-by-step explanation:

Answer:

I think the answer is A.

Step-by-step explanation:

After graphing it in Desmos, I decided model A was better, and that it was non-random.

Answer:

The correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.

Step-by-step explanation:

Consider the provided data.

The table shows the relationship between the diameter, x, in inches, and the height, y, in feet, of trees in a national park.

The residual plot for the table is shown in figure 1:

Now, consider the model 1: y = 1.04 x + 61.92

The residual of the above model is shown in figure 2:

Consider the model 1: y = 1.21 x + 58.4

The residual of the above model is shown in figure 3:

Now observe the figure 4 which compare all the three residuals.

By comparing the residual of all the three models it can be concluded that 'Model 2 has a random pattern and is a good fit for the data.

Therefore, the correct option is A) The residual plot for model 2 has a random pattern and is a good fit for the data.

Answer:

[tex]\frac{q}{360}[/tex] × π10 = 7

Explanation:

The formula to find arc length is [tex]\frac{x}{360}[/tex] × [tex]\pi r^{2}[/tex]

Simply plug in radius and arc length to get your equation.

Answer:

Central angle = 80.21°

Step-by-step explanation:

The arc length in circle is the product of radius and central angle made by the arc in radians.

That is

              l = rθ

Here given the values r = 5 ft and l = 7 ft

Substituting

             7 = 5 x θ

             θ = 1.4 radians

             [tex]\theta =1.4\times \frac{180}{\pi }=80.21^0[/tex]

Central angle = 80.21°

Answer:

[tex]\frac{3}{9}=\frac{4}{x}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

Triangle XVW is similar to triangle XZY

therefore

[tex]\frac{YZ}{VW}=\frac{XZ}{XV}[/tex]

substitute the given values

[tex]\frac{x}{4}=\frac{9}{3}[/tex]

[tex]x=3*4=12\ miles[/tex]

Answer:

A

Step-by-step explanation:

Answer: Probability theory would be my best guess, but I would need more information to be able to fully answer this question.

Step-by-step explanation:

The range of (g * f)(x) is all real numbers (ℝ).

Composing functions: We first need to understand that (g * f)(x) refers to the composition of g and f, where f is evaluated first and then its output is used as the input for g. So, (g * f)(x) = g(f(x)) = g(e^x).

Analyzing g(e^x): The function g(x) simply subtracts 2 from its input. Since e^x is a real number for all real values of x, g(e^x) will also be a real number for all real values of x.

Range of the composed function: Therefore, as g(e^x) can take any real value, the range of (g * f)(x) will be all possible outputs of g(e^x), which is all real numbers (ℝ).

In simpler terms, no matter what real number you input into f(x), the final output after applying g(x) will always be a real number. This is because the subtraction in g(x) doesn't restrict the output in any way.

Answer:

B. 29400

Step-by-step explanation:

If there is already 25,920 beds and there is 13 hospitals with 268 beds each, 268 x 13= 3484 and add that to how many beds there already are and youll have about 29400

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

What PEMDAS stands for is that in a mathematical equation, parentheses has the priority of being solved. The second priority goes to exponents, then Multiplication and Division, and then finally Addition and Subtraction.

[tex]\text{Hey there!}[/tex]

[tex]\text{The P stands for parentheses}[/tex]

[tex]\text{The E stands for exponents}[/tex]

[tex]\text{The M stands for multiplication/multiply}[/tex]

[tex]\text{The D stands for division/divide}[/tex]

[tex]\text{The A stands for Addition/Add}[/tex]

[tex]\text{The S stands for Subtraction/Subtract}[/tex]

[tex]\text{Some people refer to it as: (P)lease (E)xcuse (M)y (D)ear (A)unt (S)ally}[/tex]  [tex]\text{method for the abbreviations}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

The first one is not a function

The second is a function

Third not a function

Fourth is a function

Step-by-step explanation:

Answer: The answer has 3 forms!

I hope that this helps! :D

ANSWER

[tex]x = 3. \bar3[/tex]

EXPLANATION

The given equation is

[tex]6 = 2(x + 8) - 5x[/tex]

We expand to get,

[tex]6 = 2x + 16 - 5x[/tex]

We combine similar terms,

[tex]5x - 2x = 16 - 6[/tex]

[tex]3x = 10[/tex]

[tex]x = \frac{10}{3} [/tex]

[tex]x = 3 \frac{1}{3} [/tex]

[tex]x = 3. \bar3[/tex]

Answer:

The missing exponent is 5^7

Step-by-step explanation:

5^11/5^?=5^4

1. Subtract the exponents from each other.

11-4=7

2. Plug 7 in as the exponent.

5^11/5^7

3. 11-7=4 therefore, 5^11/5^7 equals 5^4.

Answer:

Step-by-step explanation:

[tex]\text{We know:}\ \dfrac{a^n}{a^m}=a^{n-m}.\\\\\dfrac{5^{11}}{5^{?}}=5^4\\\\5^{11-?}=5^4\to?=7\ \text{because}\ 11-7=4[/tex]

Answer:

Third choice.

The right correspondence is [tex]\angle CDB \cong \angle ECD[/tex]

Step-by-step explanation:

The third choice is not true, that is

[tex]\angle CDB[/tex] NOT corresponds to [tex]\angle ECD[/tex]

If [tex]\triangle CBD \sim \triangle CDE[/tex], then corresponding sides are proportional, and corresponding angles are congruent. The corresponding angle of [tex]\angle CDB[/tex] is

[tex]\angle CDB \cong \angle ECD[/tex]

Therefore, the third option shows a wrong correspondence, that's the right choice in this case, because it doesn't express a valid correspondence.

To find the zeros set the equation equal to zero:

x^2 - 5x +4 = 0

Factor:

(x-4) (x-1) = 0

Now solve each set of parenthesis so that they equal zero:

(x-4) = 0, x =4

(x-1) = 0, x = 1

The zeros are 1,4

Answer:

The answer is 20

Step-by-step explanation:

1). order them from least to greatest

2). cancel one number from each side until you get the middle number

Answer:

x^2 +6x +8

Step-by-step explanation:

The zeros of the graphed function appear to be (-4, 0) and (-2, 0). It appears the vertex is (-3, -1).

The standard form of the function with zeros p and q is ...

(x -p)(x -q) = x^2 -(p+q)x +pq

So, for zeros p=-4, q=-2, the standard form is ...

x^2 -(-4-2)x +(-4)(-2) = x^2 +6x +8

We can check to make sure the above vertex point satisfies this function:

(-3)^2 +6(-3) +8 = 9 -18 +8 = -1

The vertex satisfies the function we wrote, so there are no additional vertical scale factors required.

The function is ...

y = x^2 +6x +8

Answer:

2(x^2 + 4x - 28) = 0.

The length of the missing sides are:

4√2 units.

or 5.66 units ( to the nearest hundredth).

Step-by-step explanation:

Applying the Pythagoras Theorem:

8^2 = (x + 2)^2 + (x + 2)^2

2(x^2 + 4x + 4) = 64

2x^2 + 8x + 8 - 64 = 0

2x^2 + 8x - 56 = 0

2(x^2 + 4x - 28) = 0  models the situation.

Solving:

x = [- 4 +/- √(4^2-4*1*-28)]  / 2

= (-4 +/- √128) / 2

= (-4 + 8√2) / 2 ,   (-4 - 8√2) / 2  (we ignore this negative root).

= -2 + 4√2.

This is 3.66 to the nearest hundredth.

So the  length of the 2 equal sides is 2 + (- 2 + 4√2) = 4√2.

or  5.66 to the nearest hundredth.

Answer:

Lines have different slopes but same y -intercepts, c = -7

Step-by-step explanation:

The easiest way to see the relationship between the two lines is to transform them both into slope-intercept form, which is

y = mx + c

Equation 1

y = 3x − 7

Equation 2

y = -4x − 7

Lines have different slopes but same y -intercepts, c = -7

If two lines have different slopes, they cannot be the same line. However, if they share a y-intercept, that means they cross the y -axis at the same y value. Since the x value is constant on the y-axis (0), they also share an x-value here.

Answer: same y-intercept

Step-by-step explanation:

Answer:

(E) is the homogeneous mixture

Answer:

A; 8.60

Step-by-step explanation:

[tex]a^{2} +b^{2} = c^{2}[/tex]

[tex]7^{2} + 5^{2} = c^{2}[/tex]

[tex]49+25=c^{2}[/tex]

[tex]74=c^{2}[/tex]

[tex]\sqrt{74} =c[/tex]

8.60 = c

Answer:

8.40 cm

Step-by-step explanation:

7^2+5^2=x^2

49+25=x^2

74=x^2

x≈8.6

Answer:

The required inequality is [tex]6+4p>17[/tex].

Step-by-step explanation:

Let p represent the number of runs per inning.

It is given that the team scores the same number of runs per inning and the other team did not score any more points. So, the total score of other team after last four inning is 17.

Kim's team total score in last four inning is 4p. So, the total score of Kim's team after last four inning is

[tex]6+4p[/tex]

Kim's team win if the total score of other team after last four inning is less than the Kim's team.

[tex]6+4p>17[/tex]

Therefore the required inequality is [tex]6+4p>17[/tex].

Answer:

6+4p>17

Step-by-step explanation:

3 per inning

Answer:

Height of tree = 39.2 ft

Step-by-step explanation:

The relationship between the height of an object and the length of it's shadow is directly proportional.

So:

[tex]\frac{4}{2.8} =\frac{h}{27.44}[/tex]

h = Height of tree in feet

Cross multiply

2.8h = 4 · 27.44

Simplify

2.8h = 109.76

÷2.8 both sides

h = 39.2

Height of tree = 39.2 ft

The height  of a tree that cast a shadow of 27.44 ft is 39.2 ft

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that  a 4 ft stick cast a shadow of 2.8 ft.

We have to find the height of a tree that cast a shadow of 27.44 ft

Let us consider x as the  height of a tree that cast a shadow of 27.44 ft.

Let us form a proportional equation

4/2.8=x/27.44

Apply cross multiplication.

4×27.44=2.8x

109.76=2.8x

Divide both sides by 2.8

x=109.76/2.8

x=39.2

Hence, the height  of a tree that cast a shadow of 27.44 ft is 39.2 ft.

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Answer:

B(-5,-2) is the answer of the times

The perimeter of ΔABC is 20 + 2/10 units or 20.2 units.

To find the perimeter of a triangle, you need to add up the lengths of all three sides. Let's say the three sides of the triangle are a, b, and c, then the perimeter P is:

P = a + b + c

For example, if a triangle has sides of length 5 cm, 7 cm, and 9 cm, then its perimeter is:

P = 5 + 7 + 9

= 21 cm

So the perimeter of the triangle in general depends on the lengths of its sides.

Here in the Question,

we can calculate the length of BC using the Pythagorean theorem:

AC^2 + BC^2 = AB^2

(2/10)^2 + BC^2 = 10^2

4/100 + BC^2 = 100

BC^2 = 100 - 4/100

BC^2 = 9956/100

BC = sqrt(9956)/10

So the perimeter of ΔABC is:

AB + AC + BC = 10 + 2/10 + sqrt(9956)/10

= 100/10 + 2/10 + sqrt(9956)/10

= (100 + 2 + sqrt(9956))/10

= (102 + sqrt(9956))/10

≈ 20.2 units (rounded to one decimal place)

Therefore, the answer is 20 + 2/10 units or 20.2 units.

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Answer:

    ∠D = 63°

Step-by-step explanation:

Because all four corners of the quadrilateral rest on the circumference of the circle, then BIRD is a cyclic quadrilateral (circle theorem).

According to circle theorem, opposite angles of a cyclic quadrilateral are supplementary (sum to 180°).

∴  ∠I + ∠D = 180°

       ⇒ ∠D = 180° - ∠I

       ⇒ ∠D = 180° - 117°  (since ∡I = 117°)

        ∴ ∠D = 63°

Answer:

63

Step-by-step explanation:

Answer:

Step-by-step explanation:

squirrel speed (r) x seconds (3)  has to be more than 34 feet

3r is greater than 34

r is greater than 11.3

34 / 3 = 11.333

11.3 (squirrels speed) x 3 (seconds) = 33.9 feet

the squirrel can run faster than 11.3

Answer:

A). Option A

B). Option B

C). Option B

Step-by-step explanation:

A). A squirrel runs across a road in 3 seconds.

Width of the road is more than 34 feet.

We have to calculate the squirrel speed.

Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

           = [tex]\frac{34}{3}[/tex]

Since distance is more that 34 so the speed will be more than [tex]\frac{34}{3}[/tex]

This is because Speed ∝ Distance.

Let r is the speed of squirrel.

r > [tex]\frac{34}{3}[/tex]

3r > 34

Option A is the correct option.

B). Inequality is 3r > 34

r > [tex]\frac{34}{3}[/tex]

r > 11.3

Option B is the answer.

C). The squirrel can run at faster than 11.3 feet per second.

Option B.

Answer:

$67 = $29 + $ x

Step-by-step explanation:

Given that on Saturday morning Owen earned= $29

End of afternoon amount total earned was= $67

Let's find the amount earned in the afternoon=?

Let's take the amount earned in the afternoon to be =$ x

Equation for total amount earned by the end of afternoon= $29 + $x

But we know total amount earned by end of afternoon was=$67 hence

the equation to determine afternoon amount will be;

$67 = $29 + $ x ----------------------------go ahead and solve for x

$67-$29 = $ x

$ 38 = x

Answer:

[tex](x-7)^2+(y-4)^2=25[/tex]

Step-by-step explanation:

The circle has diameter endpoints of ( 4, 8 ) and (10, 16 ).

The midpoint of the diameter is the center

[tex](\frac{4+10}{2},\frac{8+16}{2})[/tex]

[tex](\frac{14}{2},\frac{24}{2})[/tex]

[tex](7,12)[/tex]

The radius is the distance from the center to any point on the circumference.

[tex]r=\sqrt{(7-4)^2+(12-8)^2}[/tex]

[tex]r=\sqrt{(3)^2+(4)^2}[/tex]

[tex]r=\sqrt{9+16}[/tex]

[tex]r=\sqrt{25}=5[/tex]

The equation of the circle with center (h,k) and radius r is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We plug in the values to get:

[tex](x-7)^2+(y-4)^2=5^2[/tex]

[tex](x-7)^2+(y-4)^2=25[/tex]

Answer:

The equation of the circle is (x - 7)² + (y - 12)² = 25

Step-by-step explanation:

* Lets revise the equation of the circle

- The equation of the circle which has center (h , k) is:

 (x - h)² + (y - k)² = r²

- The endpoints of a diameter re (4 , 8) and (10 , 16)

- The center of the circle is the mid-point of the diameter

* Lets revise the rule of the mid point to get the center of the circle

 and revise the rule of the distance to get the length of the diameter

- The mid point (x , y) of segment has endpoints (x1 , y1) and (x2 , y2) is

 x = (x1 + x2)/2  and y = (y1 + y2)/2

- The distance between the two point (x1 , y1) and (x2 , y2) is:

  d = √[(x2 - x1)² + (y2 - y1)²]

* Now lets find the center of the circle

∵ (h , k) is the mid-point of the diameter

∵ (4 , 8) is (x1 , y1) and (10 , 16) is (x2 , y2)

∴ h = (4 + 10)/2 = 14/2 = 7

∴ k = (8 + 16)/2 = 24/2 = 12

∴ The center of the circle is (7 , 12)

∵ The length of the diameter = √[(10 - 4)² + (16 - 8)²

∴ d = √[6² + 8²] = √[36 + 64] = √100 = 10

∵ The radius = 1/2 the diameter

∴ r = 1/2 (10) = 5

* Lets write the equation of the circle

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ h = 7 , k = 12 , r = 5

∴ The equation of the circle is (x - 7)² + (y - 12)² = 5²

∴ The equation of the circle is (x - 7)² + (y - 12)² = 25

Answer:

D

Step-by-step explanation:

Counting from 28 to 44, that is more than 27 miles

28, 31, 32, 33, 35, 39, 42, 43, 44

That is 9 ran more than 27 miles

9 students ran more than 27 miles.

The correct option is D.

A stem and leaf plot, often known as a stem plot, is a technique for classifying discrete or continuous variables. A stem and leaf plot organises data as it is obtained. A stem and leaf plot is similar to a bar graph. The name comes from the fact that each number in the data is divided into a stem and a leaf.

We have,

A stem and leaf plot below shows the number of miles run by members of the cross country team.

From the Leaf plot we can write the data as

5, 6, 12, 14, 19, 22, 26, 27, 28, 31, 32, 33, 35, 39, 42, 43, 44

Now, Counting from 28 to 44, that is more than 27 miles

28, 31, 32, 33, 35, 39, 42, 43, 44

So, there is 9 ran more than 27 miles.

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