4. A cylindrical hole is drilled through a wooden block that is in the shape of a rectangular prism. Find thevolume of the resulting solid. (3pts)||3 cm10.5 cmI15 cm12.4 cm
Answers
Question:
Solution:
Notice that the volume of the prism is:
[tex]V1\text{ = }whl\text{ = (12.4) x (10.5) x (15) = 1953}[/tex]on the other hand, the volume of the cylinder is:
[tex]V_2=\pi r^2h=\pi(3^2)15=135\pi\approx424.1_{}[/tex]now, we know the following formula
The volume of the resulting solid=Volume of prism - volume of cylithe nder. Then
, the correct answer is:
[tex]V=V_1-V_2\text{ = 1953-424.1 = }1528.88[/tex]thus, the correct answer is:
[tex]V=\text{ }1528.88[/tex]
Related Questions
Find the ending balance by using simple interest$1,900 at 5.9% for 2 and three fourths years
Answers
In general, the simple interest formula is
[tex]\begin{gathered} A=P(1+rt) \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ annual interest rate} \\ t\rightarrow\text{ number of years} \end{gathered}[/tex]Thus, in our case,
[tex]P=1900,r=5.9\%=0.059,t=2.75[/tex]Therefore, finding A,
[tex]\begin{gathered} \Rightarrow A=1900(1+0.059*2.75) \\ \Rightarrow A=2208.275 \end{gathered}[/tex]The exact answer is $2208.275
I need help filling in the blanks in the problem I appreciate it.
Answers
The formula for calculating binomial probability is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n represents number of trials
p represents probability of success
q represents probability of failure
x represents number of successes
From the information given,
n = 5
p = 0.479
q = 1 - p = 1 - 0.479 = 0.521
For x = k = 0,
P(x = k = 0) = 5C0 * 0.479^0 * 0.521^(5 - 0)
P(x = k = 0) = 0.0384
For x = k = 1,
P(x = k = 1) = 5C1 * 0.479^1 * 0.521^(5 - 1)
P(x = k = 1) = 0.1765
For x = k = 2,
P(x = k = 2) = 5C2 * 0.479^2 * 0.521^(5 - 2)
P(x = k = 2) = 0.3245
For x = k = 3,
P(x = k = 3) = 5C3 * 0.479^3 * 0.521^(5 - 3)
P(x = k = 3) = 0.2983
For x = k = 4,
P(x = k = 4) = 5C4 * 0.479^4 * 0.521^(5 - 4)
P(x = k = 4) = 0.1371
For x = k = 5,
P(x = k = 5) = 5C5 * 0.479^5 * 0.521^(5 - 5)
P(x = k = 5) = 0.0252
The ratio of the height to the base of a skateboard kicker ramp must be 4:1 chose all that apply
Answers
We are given various skateboard kicker ramp with different height and base
For the first triangle,
The heigth = 3 ft
Base = 12 ft
The ratio of height to base = 3/12
= 1 : 4..
Second figure,
The height = 1 ft
Base = 1.5 ft
[tex]\begin{gathered} \text{Ratio of height to base = }\frac{6}{1.5} \\ 1.5\text{ = }\frac{3}{2} \\ \text{Ratio = }\frac{6}{\frac{3}{2}} \\ \text{Ratio = }\frac{6\text{ x 2}}{3} \\ \text{Ratio = }\frac{12}{3} \\ \text{Ratio = }4\text{ : 1} \end{gathered}[/tex]Only the first figure and the second figure will give you 4 : 1 as the ratio of hei
What is the image of (-1,1) when reflected across the line y=x?
Answers
Answer:
(1,-1)
Step-by-step explanation
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.
Therefore, the image of (-1,1) is (1,-1)
The Roman numeral which represents the number in standard form 1,630 is:MCCCCCCXXX.MDCXXX.MCDXXX.MCCCXXX.
Answers
The roman number for 1000 is M.
The roman number for 600 is DC. (In this case we have to remember that the D represents 500 and C represents 100, then their sum 600 is DC).
The roman number for 30 is XXX. (X represents 10, then 30 is represented by XXX).
Therefore, the roman numeral for 1630 is MDCXXX
Sophie says, "To find 8 X 8, I can find 8 X (4 + 4)."Do you agree? Explain.3rd grade subject
Answers
Step 1
Given:
[tex]8\times8[/tex]Required:
[tex]\begin{gathered} To\text{ agre}e\text{ that if I can find 8}\times(4+4)_{} \\ \text{then I can find 8}\times8 \end{gathered}[/tex]Step 2
Find out if you agree or disagree
[tex]\begin{gathered} 8\times(4+4) \\ =\text{ (8}\times4)+(8\times4) \\ =\text{ 32 + 32 = 64} \\ or \\ 8\times(4+4) \\ \text{But (4+4) = 8} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ 8\times(4+4)\text{ = 8}\times8 \\ \text{Therefore, To find 8}\times8,\text{ I can find 8 }\times(4+4) \end{gathered}[/tex]Hence, I agree.
determine how many miles from the terminal the two types of pipe should meet so that the total cost is minimized
Answers
ANSWER:
24 miles
STEP-BY-STEP EXPLANATION:
The first thing is to make a graph of the situation, like this:
Therefore, the function of total cost will be:
[tex]C(x)=143000\cdot\sqrt[]{x^2+12^2}+55000\cdot(29-x)[/tex]To minimize we must calculate the derivative of the function, like this:
[tex]\begin{gathered} C^{\prime}(x)=\frac{d}{dx}143000\cdot\sqrt[]{x^2+12^2}+55000\cdot(29-x) \\ C^{\prime}(x)=\frac{143000d}{\sqrt[]{x^2+144}}-55000 \end{gathered}[/tex]Now we set the derivative equal to 0 and solve for d, like this:
[tex]\begin{gathered} \frac{143000d}{\sqrt[]{x^2+144}}=55000 \\ 143000x=55000\sqrt[]{x^2+144} \\ 143^2x^2=55^2\cdot(x^2+144) \\ 20449x^2=3025x^2+435600 \\ 20449x^2-3025x^2=435600 \\ 17424x^2=435600 \\ x^2=\frac{435600}{17424} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]Distance from terminal the two types of pipe meet is 29 - x, therefore would be:
[tex]\begin{gathered} d=29-5 \\ d=24\text{ miles} \end{gathered}[/tex]what is 2.2 in a fraction
Answers
To find the fraction form of 2.2
First separate, the whole number 2 from the decimal
Then write ;
[tex]\frac{0.2}{1}[/tex]since there is only one number after the decimal point, we will multiply the numerator and denominator by 10
That is;
[tex]\frac{0.2\times10}{1\times10}[/tex][tex]=\frac{2}{10}\text{ =}\frac{1}{5}[/tex]Join the fraction and the whole number part together
[tex]2.2\text{ = 2}\frac{1}{5}[/tex]Find the common difference of the arithmetic sequence 25, 31, 37, 43,OA. 8B.-6OC. 6D.-5Reset Selection
Answers
Given
The Arithmetic sequence,
25, 31, 37, 43.
To find:
The commen difference of the arithmetic sequence.
Explanation:
It is given that,
The Arithmetic sequence,
25, 31, 37, 43.
That implies,
[tex]\begin{gathered} Common\text{ }difference=31-25 \\ =6 \end{gathered}[/tex]Hence, the common difference is 6.
i need help with this asap PLEASE CHECK WORK WHEN FINISHED question 8
Answers
Answer:
32,767 pennies
Explanation:
The number of pennies saved by Joe for the first four days forms the sequence below:
[tex]1,2,4,8\cdots[/tex]We want to determine the total size of Joe's collection on the 15th day.
The sequence above forms a geometric sequence in which:
• The first term, a1 = 1
,• The common ratio, r = 2/1=4/2=2
The sum of a geometric sequence is determined using the formula:
[tex]S_n=\frac{a_1(r^n-1)}{r-1},r>1[/tex]On the 15th day: n=15
[tex]\begin{gathered} S_{15}=\frac{1(2^{15}-1)}{2-1} \\ =2^{15}-1 \\ =32768-1 \\ =32767 \end{gathered}[/tex]If Joe continues with this pattern, he will have 32,767 pennies on the 15th day.
The diameter of a circle is 20 inches. What is the area?Give the exact answer in simplest form.___ square inches.
Answers
Answer
Area = 314 square inches
Explanation
The area of a circle is given as
Area = πr²
π = pi = 3.14
r = radius of the circle = ½ (Diameter) = ½ (20) = 10 inches
Area = πr²
Area = 3.14 × (10²)
Area = 314 square inches
Hope this Helps!!!
Evaluate:10 - x + y / 2if x=5 and y=2
Answers
Given data:
The given expression is 10-x +y/2.
The given value of x is x=5.
The given value of y=2.
Substitute the given values in the expression.
[tex]\begin{gathered} 10-5+\frac{2}{2}=10-5+1 \\ =6 \end{gathered}[/tex]Thus, the value of the given expression is 6.
The penny size of a nail indicates the length of the nail. The penny size d is given by the literal equation d=4n-2, where n is the length (in inches) of the nail.A) Solve the equation for n.B) use the equation from part a) to find the length of nails with the following penny sizes: 3, 6, and 10.
Answers
Given: The penny size d is given by the equation
[tex]d=4n-2[/tex]where n is the length of the nail.
Required: a) To solve the equation for n
b) To use the equation to find out the length of the nail with the following penny sizes: 3, 6, and 10.
Explanation: The given equation can be solved for n as follows
[tex]\begin{gathered} d-4n=-2 \\ -4n=-2-d \\ 4n=2+d \\ n=\frac{2+d}{4} \end{gathered}[/tex]Now putting the value of d=3 we get
[tex]\begin{gathered} n=\frac{2+3}{4} \\ n=\frac{5}{4} \end{gathered}[/tex]Again putting d=6 we get
[tex]n=\frac{2+6}{4}[/tex][tex]\begin{gathered} n=\frac{8}{4} \\ n=2 \end{gathered}[/tex]Finally putting d=10 we get
[tex]\begin{gathered} n=\frac{2+10}{4} \\ n=3 \end{gathered}[/tex]Final Answer: a) The equation for n is
[tex]n=\frac{2+d}{4}[/tex]b) The length of the nail with penny sizes 3,6, and 10 is 5/4, 2, and 3 respectively.
How much salsa is missing from the can below? Hint: You may need to subtract the heights. 5 cm for 10 cm
Answers
Answer
Amount of salsa missing = 471.3 cm³
Explanation
The volume of a cylinder is given as
Volume = πr²h
π = 3.142
For the missing salsa,
r = radius of the cylinder = 5 cm
h = height of the missing salsa = 10 - 4 = 6 cm
Volume = πr²h
Volume = (3.142) (5²) (6) = 471.3 cm³
Hope this Helps!!!
Jack is 15 ft tall and produces a shadow 10 ft long is being stalked produces a shadow a hundred feet long how tall is jack beanstalk??
Answers
Let the height of the beanstalk be h
from the diagram,
[tex]\begin{gathered} \tan \text{ }\theta=\frac{15}{10}=\text{ 1.5} \\ \theta=\text{ }\tan ^{-1}1.5=56.3^0 \end{gathered}[/tex]Also,
[tex]\begin{gathered} \tan \text{ }\theta=\frac{h}{100} \\ 1.5=\frac{h}{100} \\ h=1.5\text{ x 100} \\ h=150\text{ ft} \end{gathered}[/tex]An advertisement says that during a sale you can at least save $50 on a suit. The most expensive suit sold for $249 during the sale. How much did the suit sell for before the sale?
Answers
Let x be the cost before the sale, since during the sale you can at least save $50, the cost before the sale was
[tex]x\ge\text{ \$249+\$50}[/tex]Therefore, the suit cost before the sale was
[tex]x\ge\text{ \$299}[/tex]that is, it costs greater or equal to $299
3 State if the two triangles are congruent or not congruent. If they are congruent, state the theorem (one of the five) that proves they are congruent. Show Your Work
Answers
First we are going to mention the postulate. It is going to be the SAS theorem.
As we can see in the image both triangles share one side, and since it is a parallelogram the hypotenuse is equal for both. So, we have 2 equal sides. And we can see each triangle has one right angle. So , the conditions of the SAS theorem are fulfilled.
4 movie tickets cost $30 5 concert tickets cost $36.50 does the movie or the concert cost less per ticket how much less
Answers
Solution;
[tex]\begin{gathered} 4\text{ movie tickets cost 30} \\ 1\text{ movie ticket=}\frac{30}{4} \\ 1\text{ movie ticket=\$7.50} \end{gathered}[/tex][tex]\begin{gathered} 5\text{ concert tickets cost 36.50} \\ 1\text{ cconcert ticket=}\frac{36.50}{5} \\ 1\text{ concert ticket=\$7.30} \end{gathered}[/tex]This means the concert ticket costs less per ticket and the difference is,
[tex]\begin{gathered} \text{Difference}=7.50-7.30 \\ \text{Difference}=0.20 \end{gathered}[/tex]The concert ticket costs $0.20 less than the movie ticket
Mitch has already run 16 miles on his own, and he expects to run 1 mile during each track practice. How many track practices would it take for Mitch to run 23 miles?practices.
Answers
If he expects to run 1 mile during each track practice, the ratio of speed would be 1 mile per track. Knowing this, we just have to divide to find the answer.
[tex]\frac{23}{1}=23[/tex]Therefore, Mitch has to take 23 track practices.B ( a little 3 on the top) - 2ac + d (a little two on the top) evaluate this polynomial if a=2,b= -3,c= 4 and d = -5.
Answers
b³ - 2ac + d²
a = 2
b = -3
c = 4
d = -5
In order to evaluate the given polynomial, we need to replace each letter by its corresponding value:
b³ - 2ac + d²
(-3)³ - 2 * 2 * 4 + (-5)²
(-3) * (-3) * (-3) - 4 * 4 + (-5) * (-5)
9 * (-3) - 16 + 25 , because the product of two negative numbers equals a positive number
-27 - 16 + 25
-27 + 9
-18
Find the exact values below. If applicable, click on "Undefined."
Answers
Answer
Tan (7π/3) = √3
csc (-330°) = 2
Explanation
tan (7π/3) Note: π radians = 180°
tan [(7 x 180°)/3]
tan 420° = tan (420 - 360)° = Tan 60°
tan 60° = √3
∴ tan (7π/3) = √3
csc (-330°) = csc (-330° + 360°)
csc (30°) = 1/sin (30°) = 1 ÷ 1/2 = 2
∴ csc (-330°) = 2
M&M candy contain 50 pics, some are yellow and rest are green there are 9 yellow pieces for every green piece, how many yellow pieces are there??
Answers
We need to create a table as follows:
Yellow pieces Green pieces Yellow/Green
5 50 - 5 = 45 5/45 = 0.11
10 50 - 10 = 40 10/40 = 0.225
15 50 - 15 = 35 15/35 = 0.4286
25 50 - 25 = 25 25/25 = 1
35 50 - 35 = 15 35/15 = 2.333
45 50 - 45 = 5 45/5 = 9
We define the number of yellow pieces, then we calculate the number of green pieces taking into account that the sum of yellow and green is 50.
Finally, we found the relation between yellow and green pieces. The answer is going to be the row where the division between the yellow and green pieces is 9. Because that division tells us how many Yellow pieces are for every green piece.
Answer: 45 yellow pieces
4x+8+6x-5=33solve the equation.
Answers
Solve the equation;
[tex]\begin{gathered} 4x+8+6x-5=33 \\ \text{Collect like terms and you have;} \\ 4x+6x+8-5=33 \\ 10x+3=33 \\ \text{Subtract 3 from both sides} \\ 10x+3-3=33-3 \\ 10x=30 \\ \text{Divide both sides by 10} \\ \frac{10x}{10}=\frac{30}{10} \\ x=3 \end{gathered}[/tex]The solution is, x = 3
Mary has some boxes that are all cubes of the same size she uses 5 of the boxes to make a tower with a hight oh 115cm she puts 2 more on the pile what is the hight of the 7 box tower.now? give your answers in centimetres
Answers
The height of the 7 box tower is 161 centimeter.
Given,
The number of boxes Mary used to make a tower = 5
The height of the tower = 115 cm
Number of boxes Mary puts again on the pile = 2
We have to find the height of the new tower.
Here,
Height of one box = Height of tower / number of boxes used
= 115/5
= 23 cm
Height of one box is 23 cm.
Height of new tower = height of old tower + (number of boxes added × height of one box)
= 115 + (2 × 23)
= 115 + 46
= 161
Therefore,
The height of the 7 box tower is 161 centimeter.
Learn more about height of box here;
https://brainly.com/question/12246051
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select the correct answer Brenda has a square shaped photo frame if the area of the square frame is 123 square inches which statement is true
Answers
Since the shape of the frame is a square we know that its area is given as:
[tex]A=l^2[/tex]where l is the length of each side, plugging the value of the area into the equation and solving for l we have:
[tex]\begin{gathered} 123=l^2 \\ l=\sqrt[]{123} \\ l\approx11.09 \end{gathered}[/tex]Therefore we notice that the length of the sides is between 11 and 12 inches, hence the answer is C.
Answer: The length of the photo frame is between the 11 inches and 12 inches.
Step-by-step explanation: 123 square root = 11.0905
3.Joe solved the equation and justified each step as shown. Identify Joe’s error and fix his mistake.StepJustification Given equation Multiplication Property of Equalityx = 14Subtraction Property of Equality
Answers
His first step should be subtracting 3 from both sides of the equation(Subtraction property of equality).
[tex]\begin{gathered} 3-3+\frac{x}{2}=10-3 \\ \frac{x}{2}=7 \end{gathered}[/tex]The multiplication property of equality states that when we multiply both sides of an equation by the same number, the 2 sides remain the same.
The next step is the Multiplication property of equality
[tex]\begin{gathered} \frac{x}{2}\times2=7\times2 \\ x=14 \end{gathered}[/tex]His error is that the Multiplication Property of equality came before the Subtraction property of equality. The subtraction property of equality should come first.
find the distance traveled by a car averaging 60 miles per hour for 3 hours.
Answers
Answer:
180 miles
Explanation:
The distance can be calculated as the speed times the number of hours.
So, the distance is equal to:
[tex]s=60\text{ miles/hour }\times3\text{ hours = 180 miles}[/tex]Therefore, the distance traveled by car was 180 miles.
Try it
Use the graph and table to write the equation that
describes the line graphed.
5
y
X
4.
1
3
-2
N
2
2
-1
الم
3
0
3
4
5
4
-5
-3 2-1
- 1
5
-2
2
-3
4
The equation of the line is
y = x + 1
y=-x+1
y = -x +3
y = x + 3
Done
Answers
Given:
Find-:
Equation of a line.
Sol:
General equation of a line.
[tex]y=mx+c[/tex]Where,
[tex]\begin{gathered} m=\text{ slope} \\ \\ m=\frac{x_2-x_1}{y_2-y_1} \\ \\ c=\text{ y-intercept.} \end{gathered}[/tex]Choose any two-point then:
[tex]\begin{gathered} (-2,1)=(x_1,y_1) \\ \\ (-1,2)=(x_2,y_2) \end{gathered}[/tex]So the slope of the line is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{2-1}{-1-(-2)} \\ \\ m=\frac{1}{-1+2} \\ \\ m=1 \end{gathered}[/tex]So the equation become:
[tex]\begin{gathered} y=mx+c \\ \\ y=(1)x+c \\ \\ y=x+c \end{gathered}[/tex]So y-intercept is:
[tex]\begin{gathered} (x,y)=(-2,1) \\ \\ y=x+c \\ \\ 1=-2+c \\ \\ c=1+2 \\ \\ c=3 \end{gathered}[/tex]So final equation of a line:
[tex]\begin{gathered} y=mx+c \\ \\ m=1 \\ \\ c=3 \\ \\ y=x+3 \end{gathered}[/tex]Equation of line is y = x + 3
12) Complete the table for m(x) = 5 - X. Show your work in the space below.m(x)3.-8.6
Answers
Here we have:
m(x) = 5 - x
which is: y = m(x) = 5 -x
To solve this, substitute each value given for x in the equation.
Consider a sequence defined by the recursive rule f(1) = 15, f(n) = f(n - 1) - 6. What is the third term of the sequence?
Answers
According to the problem, the recursive rule is
[tex]\begin{gathered} f(1)=15 \\ f(n)=f(n-1)-6 \end{gathered}[/tex]This means the first term of the sequence is 15.
So, for n = 2, we have
[tex]f(2)=f(2-1)-6=f(1)-6[/tex]But, we know that f(1) = 15, so
[tex]f(2)=15-6=9[/tex]The second term is 9.
For n = 3.
[tex]f(3)=f(3-1)-6=f(2)-6[/tex]But, we know that f(2)=9, so
[tex]f(3)=9-6=3[/tex]Therefore, the third term is 3.