ind the volume of the pyramid, if the base is a square with the side 3.5 cm and height of the pyramid is 1.5 cm

Answer:

  226 ft²

Step-by-step explanation:

The surface of the figure can be considered in several parts:

a) top and bottom surfaces

b) outside surfaces

c) inside surfaces

__

The top and bottom surfaces each consist of a rectangle 8 ft by 4 ft with a 4 ft by 1 ft hole. The area of the larger rectangle without the hole is the product of its length and width:

  (8 ft)(4 ft) = 32 ft²

The area of the hole is the product of its length and width:

  (4 ft)(1 ft) = 4 ft²

Then the area of the surface around the hole is the difference of these:

  32 ft² - 4 ft² = 28 ft²

The top and bottom surfaces together have twice this area for a total of ...

  top and bottom area = 2·(28 ft²) = 56 ft²

__

The outside (lateral) area is the total area of the four rectangles that make up the sides of the figure. Each rectangle has a height of 5 ft, so we can compute the area by finding the perimeter of the figure and multiplying that by 5 ft.

The perimeter is the sum of the lengths of its top or bottom edges:

  8 ft + 4 ft + 8 ft + 4 ft = 2·(8 ft +4 ft) = 2·12 ft = 24 ft

Then the lateral area is ...

  outside lateral area = (5 ft)(24 ft) = 120 ft²

__

The area of the sides of the hole can be computed the same way. The hole is 5 ft high and its edge lengths are 1 ft and 4 ft. Then the total inside lateral area is ...

  inside lateral area = (5 ft)(2·(1 ft + 4ft)) = 50 ft²

__

So the total surface area of the solid is ...

  total area = top and bottom area + outside lateral area + inside lateral area

  total area = (56 + 120 + 50) ft²

  total area = 226 ft²

Answer:

QPR

Step-by-step explanation:

It is triangle QPR because of the order of corresponding angles.

So you would do 1/3 times 4 so that is 1 and 1/3

The total distance that was run by Runners who each ran for 1/3 of a mile​ will be 4/3.

The distance is defined as the length of the space between the two points separated from each other.

From the graph, the distance of 1/3 miles is covered by 4 runners so the total distance will be calculated as:-

Distance = 1/3  x  4

Distance = 4/3  miles

Hence the total distance that was run by Runners who each ran for 1/3 of a mile​ will be 4/3.

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Answer: well i can see 34 eyeballs in the jar, if you multipy that by pie, and then divide by 2 then multiplyb b to. the cut it into third by the mcd, (most common deenominator) you get 4216

Step-by-step explanation: i ran these numbers for weeks on weeks, please tell me if it worked i haveen't slept in days.

Answer:

6. C: {x^2 +(y-1)^2 =2; x+y = 3}

15. C: The line does not intersect the circle.

Step-by-step explanation:

The formula for the distance (d) from a point (x, y) to a line ax+by=c is ...

d = |ax+by-c|/√(a^2+b^2)

The formula for a circle centered at (h, k) with radius r is ...

(x -h)^2 +(y -k)^2 = r^2

___

6. Comparing the circle equation to the generic equation, we find (h, k) = (0, 1) and r = √2. Then we want to find the line that is distance √2 from the center of the circle. Our line equation is x+y=c for some value of c that we want to find.

d = √2 = |0 +1 -c|/√(1^2+1^2)

2 = |1-c|

±2 = 1-c

c = 1±2 = -1 or 3

The line that is tangent to the circle is the one of choice C: x+y = 3

__

The attached graph shows the lines for all 4 answer choices. The point of tangency is (1, 2), so x+y=1+2=3.

___

15. The circle is centered at (4, 1) and has radius 3. The distance from the circle center to the line is ...

d = |2(4) -(1)|/√(2^2+(-1)^2) = 7/√5 ≈ 3.13

The distance from the circle center to the line is more than the radius of the circle, so there can be no points of intersection.

__

Alternate solution

You can substitute for y using the equation of the line. Then the circle equation becomes ...

(x -4)^2 + (2x -1)^2 = 9

x^2 -8x +16 +4x^2 -4x +1 = 9

5x^2 -12x +8 = 0

The discriminant of this quadratic is ...

b^2 -4ac = (-12)^2 -4(5)(8) = 144-160 = -16

Since this value is negative, there can be no real solutions, meaning the line does not intersect the circle.

Answer:

(B) [tex]SA=72{\tex{feet^2}[/tex]

Step-by-step explanation:

Given: From the figure, it is given that the length of the base is 4 feet and slant height is 7 feet.

To find: The Surface are of Pyramid.

Solution: From the figure, it is given that the length of the base is 4 feet and slant height is 7 feet.

Now, surface area of the Pyramid is given as:

[tex]SA={\text{Area of base}+\frac{1}{2}pl[/tex]

where p is the perimeter and l is the slant height.

Now, area of base is given as:

[tex]A=4(4){\tex{ft^2}[/tex]

[tex]A=16{\tex{ft^2}[/tex]

And, the surface area is given as:

[tex]SA=16+\frac{1}{2}(4)(4)(7)[/tex]

[tex]SA=16+56[/tex]

[tex]SA=72{\tex{feet^2}[/tex]

Hence, option  B is correct.

Answer:

B 72 ft^2

Step-by-step explanation:

The area surface of a square pyramid is given by adding the area of the square that creates the base, and then the area of the 4 triangles that make up for the sides of the pyramid, so we first calculate the area of the triangle:

Area= b*h/2

Area= 4*7/2

Area=14

Now we calculate the area of the base:

Area=side*side

Area=4*4

Area=16

No we add up the four triangles plus the base:

Surface area=(Sides*4)+base

Surface area= (14*4)+16

Surface area=56+16

Surface area=72

So the surface area of the pyramid would be 72 ft^2

Final answer:

The student performed relatively better on the Geography test than on the Mathematics test, with z-scores of -1.2 and -1.5 respectively, because a higher z-score indicates a performance closer to the mean.

Explanation:

To determine on which test the student scored better relative to the other students, we must calculate the z-scores for each test.

The z-score formula is:

Z = (X - μ) /σ

Where X is the student's score, μ is the mean, and σ is the standard deviation.

For the Geography test:

Z = (56 - 80) / 20
Z = -24 / 20
Z = -1.2

For the Mathematics test:

Z = (285 - 300) / 10
Z = -15 / 10
Z = -1.5

A z-score tells us how many standard deviations an element is from the mean. The student had a z-score of -1.2 in Geography and -1.5 in Mathematics. Since a higher z-score reflects a performance that is closer to the mean, the student performed relatively better on the Geography test compared to the Mathematics test.

Answer:

If the landscaper decides not to purchase the tallest plant, then the median heights of the plants would (increase-decrease-stay the same) , but the mean height would (increase-decrease-stay the same)

Step-by-step explanation:

The Complete sentences are:

The median heights of the plants would stay the same.

The mean height would decrease.

Based on the values of each point, a dot plot visually groups the number of data points in a data set. Similar to a histogram or probability distribution function, this provides a visual representation of the data distribution.

We have,

A dot plot shows the heights of the plants a landscaper plans to purchase.

The median heights of the plants would stay the same.

If the landscaper decided not to buy the tallest plant, however the mean height would decrease.

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Answer:

The vertex form of a quadratic equation is:

[tex]f(x) = (x-3)^2+4[/tex]

the minimum value of f(x) is [tex]y=4[/tex]

Step-by-step explanation:

Given a quadratic equation of the form [tex]f (x) = ax ^ 2 + bx + c[/tex] then the x coordinate of the vertex is

[tex]x=-\frac{b}{2a}[/tex]

So for  [tex]f(x)=x^2-6x+13[/tex]

[tex]a=1\\b=-6\\c=13\\[/tex]

Therefore

The x coordinate of the vertex is:

[tex]x=-\frac{(-6)}{2(1)}[/tex]

[tex]x=3[/tex]

The y coordinate of the vertex is:

[tex]f(3)=(3)^2-6(3)+13[/tex]

[tex]y=f(3)=4[/tex]

By definition the minimum value of the quadratic function is the same as the coordinate of y of its vertex

So the minimum value  is [tex]y=4[/tex]

The vertex form of a quadratic equation is:

[tex]f(x) = a(x-h)^2+k[/tex]

Where

a is the main coefficient. [tex]a=1[/tex]

h is the x coordinate of the vertex. [tex]h=3[/tex]

k is the y coordinate of the vertex. [tex]k=4[/tex]

So the vertex form of a quadratic equation is:

[tex]f(x) = (x-3)^2+4[/tex]

Answer:

a.  [tex]f(x)=(x-3)^2+4[/tex]

b. The minimum value is 4

Step-by-step explanation:

The given function is: [tex]f(x)=x^2-6x+13[/tex]

We add and subtract half the square of the coefficient of x.

[tex]f(x)=x^2-6x+3^2-3^2+13[/tex]

This becomes: [tex]f(x)=x^2-6x+9-9+13[/tex]

The first three terms form a perfect square trinomial.

[tex]f(x)=(x-3)^2+4[/tex]

The function is now in the form:  [tex]f(x)=a(x-h)^2+k[/tex], where V(h,k) is the vertex.

Therefore the vertex is (3,4).

The minimum value  is the y-value of the vertex, which is 4.

Answer:

6

Step-by-step explanation:

Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:

120/(n+24) = (120/n) -16

Multiplying by n(n+24) gives ...

120n = 120(n+24) -16(n)(n+24)

0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms

n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller

(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic

The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.

The woman bought 6 items.

_____

Check

When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.

Answer:

a. (-3,2)

b. sqrt65

c.

Step-by-step explanation:

a. To find the center of the circle, you can think of it just like finding the midpoint between the two endpoints. To find a midpoint between two endpoints, you take the average of the x values to get the x coordinate, and you take the average of the y values to get the y coordinate of the midpoint. Therefore, if (-10, -2) is (x1, y1) and (4, 6) is (x2, y2), the midpoint/center of the circle would be:

( (x1+x2)/2, (y1+y2)/2 ). When you plug in our x and y values, you get (-3, 2).

b. To find the radius of a circle, you need to know the center/midpoint of the circle which we solved for in part a. The formula for finding the radius of a circle with the center is (x-h)^2 + (y-k)^2 = r^2 for (h, k) as the center. The coordinates of the center that we found earlier for this circle are (-3, 2). With that, we just plug in our numbers into the formula, and we get:

(x+3)^2 + (y-2)^2 = r^2. Now, to get r, we can choose one of the original two endpoints given and plug in the x and y coordinates from that point into this equation. I like (4, 6), so I'm going to plug in 4 for x and 6 for y, and so we get (4+3)^2 + (6-2)^2 = r^2 which equals 49 + 16 = r^2 when simplified. 49 plus 16 is equal to 65, so we get 65 = r^2. To finally get r, we square root both sides of the equation to get r =  sqrt65 which is already in the simplest radical form.

c. The circle equation is (x-h)^2 + (y-k)^2 = r^2, like I said in part b. Therefore, we already have our circle equation! We just plug in our center points and we get (x+3)^2 + (y-2)^2 = sqrt65. This is usually an equation a question will give you for a circle, and with this information, they will expect you to find the center (h, k) or the circle and it's radius, r.

The center of the circle with diameter endpoints P(-10, -2) and Q(4, 6) is C = (-3, 2). The radius in radical form is √65. The equation for the circle is (x + 3)² + (y - 2)² = 65.

Finding the Center and Radius of a Circle

To find the center of the circle, you need to find the midpoint of the diameter with endpoints P(-10, -2) and Q(4, 6). The midpoint formula is:

((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in our points, we get:

Center (C) = ((-10 + 4) / 2, (-2 + 6) / 2) = (-3, 2)

Finding the Radius in Radical Form

To find the radius of the circle, we calculate the distance between P and Q and then divide it by 2. The distance formula is:

√[(x2 - x1)² + (y2 - y1)²]

The distance (diameter) is √[(4 - (-10))² + (6 - (-2))²] = √[14² + 8²] = √[196 + 64] = √260. Therefore, the radius (r) is √260/2 or √65.

The Equation of the Circle

The standard form equation for a circle with a center (h, k) and radius r is (x - h)² + (y - k)² = r². Therefore, the equation for this circle, with center (-3, 2) and radius √65, is:

(x + 3)² + (y - 2)² = 65

Answer:

Step-by-step Answer:

6 reindeer, from which we fly 5, in N1 ways.

Each of the five must be arranged in N2 ways.

The total number of arrangements is therefore N1*N2 arranglements.

Note: C(n,r) = n!/((r!(n-r)!)

N1 = 6 choose 5 = C(6,5) = 6!/(5!/1!) =  6 ways

(same as number of ways to choose 1 reindeer to be left out).

N2 = 5! ways (5 choices for the first, 4 choices for the second, 3 for the third, and 2 for the fourth, and 1 for the last) = 5*4*3*2*1 = 120 ways.

So total number of arrangements

= N1 * N2 = 6 * 120 = 720 ways.

Alternatively, you can line up the 5 vacant spaces and choose the first among 6 reindeer, second among 5, third among 4, fourth among 3, and the last one among 2 for a total of

6*5*4*3*2 = 720 arrangements.

Answer:

(2,1) is the only solution to the linear equation

Step-by-step explanation:

to solve, just plug in the values given into the orignal expression. remember, the answer on the left has to be equal to the answer on the right.

(2,1)

4(2) + 3(1) = 11 --> 8 + 3 = 11 --> 11 = 11 (2,1) is a solution to the linear equation

(6,0)

4(6) + 3(0) = 11 --> 24 + 0 = 11 --> 24 ≠ 11 (6,0) is not a solution to the linear equation

(0,1)

4(0) + 3(1) = 11 --> 0 + 3 = 11 --> 3 ≠ 11 (0,1) is not a solution to the linear equation

Answer: upon itself

Step-by-step explanation: apex

Answer:

  square inch — is a unit of area, not volume

Step-by-step explanation:

Some volume measures have their own unit, like liters, cups, pints, quarts, gallons, bushels, or barrels.

Other volume units are the cube of a linear measure, such as cubic centimeters, cubic inches, cubic feet, or cubic meters.

Still other volume units are a hybrid of an area measure and a linear measure, such as acre-feet.

A measure that is the square of a linear unit is an area measure, not a volume measure.

Answer:

Step-by-step explanation:

"square inch" is a unit of area, not of volume.

[tex]f(x)=\begin{cases}5x-8&\text{for }x<0\\|-4-x|&\text{for }x\ge0\end{cases}[/tex]

The limits from either side are

[tex]\displaystyle\lim_{x\to0^-}f(x)=\lim_{x\to0}(5x-8)=-8[/tex]

[tex]\displaystyle\lim_{x\to0^+}f(x)=\lim_{x\to0}|-4-x|=\lim_{x\to0}|x+4|=|4|=4[/tex]

The one-sided limits don't match, so the limit as [tex]x\to0[/tex] does not exist.

A function assigns the values. The limit as x→0 does not exist.

A function assigns the value of each element of one set to the other specific element of another set.

The given limits can be written as,

[tex]f(x)=\left \{{5x-8\ \ \ {\rm for\ x < 0} \atop |-4-x|\ \ \ {\rm for\ x \geq 0}} \right.[/tex]

Now, the limits from either side are,

[tex]\lim_{x \to 0^-} f(x) = \lim_{x \to 0} (5x-8) = -8[/tex]

[tex]\lim_{x \to 0^+} f(x) = \lim_{x \to 0} |-4-x| = \lim_{x \to 0} |x+4|=|4| = 4[/tex]

Since one side of the limits doesn't match, so the limit as x→0 does not exist.

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Answer: x=14

Step-by-step explanation:

1. Simplify 1/5(x−4) to (x−4)/5​​.

(−x−4)/5=−2

2. Multiply both sides by 5.

−x+4=−2×5

3. Simplify 2×5 to 10.

−x+4=−10

4. Regroup terms.

4−x=−10

5. Subtract 4 from both sides.

−x=−10−4

6. Simplify −10−4 to −14.

−x=−14

7. Multiply both sides by −1.

x=14

Answer:

25

Step-by-step explanation:

You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.

Answer:

   4 yd 2 ft 5 in

Step-by-step explanation:

One straightforward way to do this is to convert to inches and back:

  28 yd 2 ft 6 in = (28 yd)(36 in/yd) + (2 ft)(12 in/ft) + 6 in

  = 1008 in + 24 in + 6 in = 1038 in

Then your division problem looks like ...

  (1038 in)/6 = 173 in

Converting this back to yards, feet, and inches can proceed like this ...

  (173 in)/(36 in/yd) = 4 yd remainder 29 in . . . . . find the number of yards first

  = 4 yd + (29 in)/(12 in/ft) = 4 yd 2 ft 5 in . . . . . then find feet and inches

Answer:

[tex]b = 60 {(1.05)}^{3} \\ b = 69.46[/tex]

B = $69.46

Step-by-step explanation:

It should be B = 69.46 but lower case was the only option given for variables.

Answer:

Option a.

I and III

Step-by-step explanation:

Observing the graph

For n=400 coats

The cost is about $2,200

and

The revenue is less than $1,400

Substitute the value of n=400 in each equation to find the solution

I Cost 1.5(400)+1,600=$2,200 ----> is ok

II Cost 4.5(400)+1,600=$3,400 ----> is not ok ( is greater than $2,200)

III Revenue 3.25(400)=$1,300 ----> is ok ( is less than $1,400)

IV Revenue 5.75(400)=$2,300 ----> is not ok ( is greater than $1,400)

therefore

The solution is I and III

Answer:

A

Step-by-step explanation:

(a) The bond pays 5% of its face value each year. That amount is ...

  0.05 × $14,000 = $700 . . . . per year

So, in 6 years, the bond pays ...

  6 × $700 = $4200

__

(b) The bond continues to pay $700 per year for the next 24 years. At the end of that time, the face value of the bond is also paid. So, the total amount paid to the bondholder in 24 years is ...

  24 × $700 + 14,000 = $16,800 +14,000 = $30,800

__

(c) The present value of the bond is the present value of the cash flows it will generate. It will pay $700 at the end of each year for 24 years, then $14,000 at the end of the 24th year. Assuming cash flows are discounted at 7.5% per year over that period, the present value will be ...

  present value of series of payments = (700/1.075)·(1.075^-24 -1)/(1.075^-1 -1)

  ... = 7688.08

  present value of final payment = 14,000·1.075^-24 = 2467.88

So, the total present value is ...

  present value of the bond = $7,688.08 +2,467.88 = $10,155.96

Answer: Third and fifth option

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Step-by-step explanation:

Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.

For example, for the following set of 7 data:

2, 3, [5], 8, 13

the median is 5.

If the data number is even, for example 10 data:

3, 5, 9, 12, [19, 21], 33, 35, 40, 69

The median is the average between the two data that are in the middle

[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]

Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example

2, 4, 4.5, 4.8, 5          Median = 4.5

2, 4, 4.5, 67, 1506     Median = 4.5

The median does not represent the difference between the highest and the lowest data.

Therefore the correct affirmations are:

3) The median is the number in the middle on an ordered set of data.

5) To find the middle of an even data set, find the average of the two middle numbers.

Answer:

B. (-2, 0) and (1, 0)

Step-by-step explanation:

The equation can be factored as ...

y = 2(x^2 +x -2) = 2(x +2)(x -1)

The x-intercepts are the values of x where y=0, so will be the values of x that make one or the other of the binomial factors zero:

x = -2

x = 1

Then the intercept points are (-2, 0) and (1, 0). . . . . . . . . matches choice B

Answer:

93.6 inch^2

Step-by-step explanation:

sides=6 side-length=6 inches Apothem= 5.2 inches Area= 6*(1/2)(6)(5.2)

The area of the regular hexagon is 93.6 square centimeter.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write area as -

V = ∫∫F(x, y) dx dy

Given is a regular hexagon with a side length of 6 cm and an apothem of approximately 5.2.

We can write the area of the regular hexagon as -

A = {3√3}/2 x a²

A = {3√3}/2 x 6 x 6

A = 93.6 square centimeter

Therefore, the area of the regular hexagon is 93.6 square centimeter.

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Answer:

F(x) < 0 , over the intervals (-∞, -0.7) and (0.76 , 2.5)

Step-by-step explanation:

The correct answer is the first option

F(x) < 0 , over the intervals (-∞, -0.7) and (0.76 , 2.5)

We can see that over those intervals, the function becomes negative.

That is, it becomes less than zero.

We can see the graph in the image below.

if the perimeter of 1/4 of the circle is 7.14, then the full circle is 4(7.14) = 28.56.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=28.56 \end{cases}\implies 28.56=2\pi r \\\\\\ \cfrac{28.56}{2\pi }=r\implies 4.55\approx r[/tex]

and the radius is the same on any location of the circle.

A quarter of a circle having a perimeter 7.14 feet has a radius of 4.55 feet.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

If a complete circle has a perimeter of 2πr, the quarter of a circle should have (2πr/4) = (1/2)πr.

Given, The perimeter of a quarter circle is 7.14 feet.

Therefore,

(1/2)πr = 7.14.

πr = 14.28.

r = 14.28/3.14.

r = 4.55 feet.

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Answer:

Step-by-step explanation:

if the temp is -8°F and you add 19 your new temp is 11°F

Final answer:

To find the final temperature after a rise of 19°F from -8°F, define the variable T as the final temperature, and use the expression T = initial temperature + temperature change, which evaluates to T = 11°F.

Explanation:

The student is asked to determine the temperature after a rise of 19°F from an initial temperature of -8°F. To solve this, let's define the variable T to represent the final temperature. The expression to find the final temperature after the rise would be:

T = initial temperature + temperature change

In this case, the initial temperature is -8°F and the temperature change is a rise of 19°F, so the expression becomes:

T = -8°F + 19°F

When we evaluate this expression:

T = 11°F

Therefore, the temperature after a rise of 19°F from -8°F is 11°F.

Answer:

2.5 inches in height

Step-by-step explanation:

Givens

water flowing = 7500 in^3 / minute

water flowing = 75000 in^3 / minute * 10 minutes

Tank diameter = 196 inches

Tank radius = 196 inches /2

Tank radius = 98 inches

h_10 minutes = ??

Formula

V = pi r^2 h

Solution

75000 = 3.14 * 98^2 * h

75000 = 3.14 * 9604 * h

75000 = 30156.56 * h

h = 75000 / 30156.56

h = 2.487 which rounded to the nearest 1/10 is

h = 2.5 inches. Seems awfully small doesn't it, considering the volume flowing in.

Answer:

86.86

Step-by-step explanation:

Another word for mean is average.  To find the mean or average, we add up all the numbers and then divide by the number of numbers

There are 7 scores

Mean = (88+91+89+94+90+64+ 92)/7

         = 608/7

         =86.85714286

To 2 decimal places ( we have to round to be accurate to 2 decimal places)

         86.86