Answers
The volume of the prism as given with dimensions is; 840cm³.
What is the volume of the prism?The prism given in the task content can be further subdivided to be represented by two rectangular prisms as follows;
First prism = 10cm by 6cm by 8cm.
Second prism = 5cm by 12cm by 6cm
Hence, the volume of the prism is; (10×6×8) + (5×12×6) = 840cm³.
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Related Questions
{x + 8y = -16
{x-3y = -5
Answers
Answer: y= -1 and x=-8
x+8y=-16
x=-8y-16
so x-3y=-5
-8-16-3y=-5
-11y-16=-5
-11y=-5+16
-11y=11
y=-1
x-3y=-5
x+3=-5
x=-8
Step-by-Step Solution:
=> x + 8y = -16 (Eq. 1)
=> x - 3y = -5 (Eq. 2)
Subtracting Eq. 2 from 1, we get :-
8y + 3y = -16 + 5
11y = -11
y = -11/11
=> y = -1
Therefore, y = -1
Substitute value of ‘y’ in Eq. 2 :-
x - 3y = -5
x - 3(-1) = -5
x - -3 = -5
x + 3 = -5
x = -5 - 3
x = -5 + -3
=> x = -8
Therefore, x = -8
Hence, x = -8 and y = -1 (-8, -1)
A competition to catch the most rainbow trout on Lake Rainbow pitched the men against the ladies. 16 men and 12 women participated. Each participant had a total of 15 attempts before they retired from the competition. It was predicted that the men would have a 9% chance of catching a rainbow trout at each attempt. One participant's experience resulted in 3 successful catches. The probability that this participant was a woman is 40%. Find the probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman.
Answers
The probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman is 0.0042.
P(woman) = 12/28
= 3/7
P(men) = 16/28
= 4/7
P(3 trouts) = P(3 trout | women)*P(woman) + P(3 trout | men)*P(man)
= P(3 trout | women)*(3/7) + (15C3 * (0.09^3)*(1-0.09)^(15*3))*(4/7)
= P(3 trout | women)*(3/7) + (0.00476)*(4/7)
P(woman | 3 trout) = P(3 trout | women)*P(woman) / P(3 trouts)
{P(3 trout | women) = p}
p*(3/7) / (p*(3/7) + (0.00476)*(4/7)) = 0.40
p*(3/7)/0.40 = (p*(3/7) + (0.00476)*(4/7))
p*((3/7)/0.40 - (3/7)) = (0.00476)*(4/7)
p = [(0.00476)*(4/7)] / [((3/7)/0.40 - (3/7))]
= 0.0042
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Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answers
If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal is 4.7
We have given that,
Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles.
We have to determine that If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal.
Based on the given conditions, formulate: 8+4x=26
Rearrange unknown terms to the left side of the equation:4x=26-8
Calculate the sum or difference:4x=18
Divide both sides of the equation by the coefficient of the variable:4x/4=18/4
Calculate the product or quotient:x=18/4
We get the result:4.7
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Answer: The answer is 6.6
Step-by-step explanation:
This year, a small business had a total revenue of $40,700. If this is 26% less than their total revenue the previous year, what was their total revenue the previous year?
Answers
So previous year x 0.74 = 40,700
Previous year = 40,700 / 0.74 = $55,000
Elias Rubio deposits three checks for $598.20, $2,274.26, and $3,248.79.
His cash consists of 75 one dollar bills, 78 five dollar bill., 83 ten-dollar
bills, 80 quarters, 32 dimes, 95 nickels, and. 5 pennies. He would like to
receive $40.00 in cash.
Answers
Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323
How much did Elias deposit in cash?This can be found as:
= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)
Solving gives:
= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05
= $1,323
Remaining part of the question:
How much did he deposit in cash?
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What is 5 ones , 38 tens , 27 hundreds , and 5 thousands? Write the number in word form and expanded form
Answers
Answer:
Eight thousand eighty five, 8000 + 80 + 5
Explanation:
Five ones, thirty-eight tens, twenty-seven hundreds, and five thousands equal to:
5 + 380 + 2700 + 5000
This is 8085 when added or eight thousand eighty-five in word form. This is also 8000 + 80 + 5 in expanded form.
what is the angle between a=7i+3j and b=4i-j
Answers
[tex]a\cdot b=(7)(4)+(3)(-1)=25\\\\|a|=\sqrt{7^{2}+3^{2}}=\sqrt{58}\\\\|b|=\sqrt{4^{2}+(-1)^{2}}=\sqrt{17}\\\\\cos \theta=\frac{25}{\sqrt{58}\sqrt{17}}\\\\\theta=\cos^{-1} \left(\frac{25}{\sqrt{58}\sqrt{17}} \right) \approx 37.235^{\circ}[/tex]
Practice Question:
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
Find (f + g)(x)
Answer Options (Choose one):
A. (f+g)(x) = -6x^3 + 8x^2 + 4x -4
B. (f+g)(x) = 6x^3 + 3x^2 - x - 8
C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8
D. (f+g)(x)= 9x^3 - x - 8
Answers
The correct option of the function is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
So,
(f + g)(x) = (3x^2 + 4x - 6) + (6x^3 - 5x^2 -2)
(f + g)(x) = 3x^2 + 4x - 6 + 6x^3 - 5x^2 - 2
Now, like terms and in order of exponent
(f + g)(x) = 6x^3 - 2x^2 + 4x - 8
Therefore, the correct option is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
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Dexter makes 40 cookies.
He eats 16 of the cookies and take the rest to school.
What percentage of the cookies does he take to school?
Answers
What is the aquare root of 0.00053361
Answers
Step-by-step explanation:
no calculator ? or what is the problem ?
I had to use the calculator too.
so, the square root of 0.00053361 is 0.0231.
25:50=4x:8. What is the value of X
Answers
Answer: X = 1
Step-by-step explanation:
25/50 = 4x/8
First, multiply both sides by 8, therefore, the 8 on the right side will be canceled out.
25*8/50 = 4x*8/8
25*8/50 = 4x
25*8 = 200
200 divided by 50 = 4
4 = 4x
After that, you just need to divide 4 on both sides, therefore, the 4 on the right side will cancel out.
4/4 = 4x/4
1 = x
X = 1
Hope I helped! :]
Solve the following inequalities and represent the solution on the number line.
d) 5x ≥ 15
e) 3(2x + 1) ≤ 15
Answers
d) 5x ≥ 15
Let's solve your inequality step-by-step.
5x≥15
Step 1: Divide both sides by 5.
[tex]\frac{5x}{5} \geq \frac{15}{5}[/tex]
[tex]x\geq 3[/tex]
(Attachment #1)
e) 3(2x + 1) ≤ 15
Let's solve your inequality step-by-step.
3(2x+1)≤15
Step 1: Simplify both sides of the inequality.
6x+3≤15
Step 2: Subtract 3 from both sides.
6x+3−3≤15−3
6x≤12
Step 3: Divide both sides by 6.
[tex]\frac{6x}{6} \leq \frac{12}{6}[/tex]
[tex]x\leq 2[/tex]
(Attachment #2)
2. Compare and contrast a function and its inverse. Represent your
answer in a table of values and in a mapping diagram.
Answers
The table of values for the comparison of a function and its inverse function is shown in the image attached below.
What is an inverse function?An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).
In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:
f(-6) = -10f⁻¹(-10) = -6f⁻¹(f(3)) = -9.Read more on inverse function here: https://brainly.com/question/15635761
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Can you solve this question and explain it for me? Thank you
Answers
By direct observation on the graph and concept of relative minimum, we conclude that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).
How to determine the relative minimum of a given graph
Let be f a function that exists in a interval [a, b], there is a value c such that f(c) < f(x), for x ≠ c and x ∈ [a, b]. In this case, f(c) is the relative minimum of f. By direct observation, we find that the relative minimum of the graph is contained by the point (x, y) = (3, - 17).
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Dry concrete can be made by mixing sand, gravel and cement
in the ratio 1: 2: 3. If you want 1800 kg of dry concrete,
how much of each will you need? Give your answers in
kilograms (kg).
Answers
Gravel is 2/6 of mixture. 2/6 x 1800 = 600 kg
Cement is 3/6 of mixture. 3/6 x 1800 = 900 kg
A ratio shows how many times one number contains another.
Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is
[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]
The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]
And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]
What is the ratio ?
A ratio is an ordered pair of numbers [tex]a[/tex] and [tex]b[/tex], written [tex]\frac{a}{b}[/tex] where [tex]b[/tex] does not equal [tex]0[/tex]. A proportion is an equation in which two ratios are set equal to each other.
Here the given ratio is [tex]1:2:3[/tex].
Here given that,
The dry concrete is [tex]1800kg[/tex].
And the multiplication of the ratio is [tex]1[/tex]×[tex]2[/tex]×[tex]3=6[/tex]
Hence, the sand is in the ratio [tex]\frac{1}{6}[/tex] of the mixture is
[tex]\frac{1}{6}[/tex]×[tex]1800=300kg[/tex]
The Gravel is in the ratio [tex]\frac{2}{6}[/tex]×[tex]1800=600kg[/tex]
And the cement is in ratio [tex]\frac{3}{6}[/tex]×[tex]1800=900kg[/tex]
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Solve the quadratic function by factoring.
y = 4x² 13x + 10
Answers
Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]
Step-by-step explanation:
To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that
[tex](4)(10) = 40[/tex]
Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40
Now split 13x into 5x+8x and solve by grouping
[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]
Factor out the GCF in each quantity
[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]
Now group x+2 together
[tex](x+2)(4x+5)[/tex]
Finally, set each factor equal to 0 and solve for x
[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]
Please help! To solve the equation 1.75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
Answers
Answer:
C
Step-by-step explanation:
1.75n = 7 ( to isolate n divide both sides by 1.75 )
n = [tex]\frac{7}{1.75}[/tex] = 4
Answer:
c.) Divide by 1.75
Step-by-step explanation:
Given equation:
⇒ 1.75n = 7
Here the coefficient of n which is 1.75 needs to be removed. There is only one way of doing that - by dividing both sides by 1.75.
When done so:
⇒ 1.75n/1.75 = 7/1.75
⇒ n = 4
Six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the probability that a girl wins the first place award while boys will receive the second and third place awards? express your answer as a percent.
Answers
Answer:
the probability is 10%
Step-by-step explanation:
(Giving 80 points, Please do not answer if you don't know. The second and third answer are not 4 btw)
Point A is on the point −6 and Point B is on the point 0. Let's use the Ruler Postulate to find the length of AB¯¯¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯¯¯ is 6. We can also write this as AB=6 or mAB¯¯¯¯=6.
Find the Length of CD¯¯¯¯
Now, let's find the length of CD¯¯¯¯. Point C is on the point 4 and Point D is on the point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯¯ is 4. We can also write this as CD=4 or mCD¯¯¯=4
Your Turn
1. What is the length of BC¯¯¯? 4
2. What is the length of AC¯¯¯¯?
3. What is the length of AD¯¯¯¯?
Answers
Answer:
1. 4
2. 10
3. 14
Step-by-step explanation:
A = -6
B = 0
C = 4
D = 8
1. BC = |0 - 4| = 4
2. AC = |-6 - 4| = |-10| = 10
3. AD = |-6 - 8| = |-14| = 14
Answer:
1. BC = 4
2. AC = 10
3. AD = 14
Step-by-step explanation:
Ruler Postulate
The distance between any two points on a number line is their difference.
Question 1
Given:
Point B = 0Point C = 4Therefore, using the Ruler Postulate:
⇒ BC = |b - c|
⇒ BC = |0 - 4|
⇒ BC = |-4|
⇒ BC = 4
Question 2
Given:
Point A = -6Point C = 4Therefore, using the Ruler Postulate:
⇒ AC = |a - c|
⇒ AC = |-6 - 4|
⇒ AC = |-10|
⇒ AC = 10
Question 3
Given:
Point A = -6Point D = 8Therefore, using the Ruler Postulate:
⇒ AD = |a - d|
⇒ AD = |-6 - 8|
⇒ AD = |-14|
⇒ AD = 14
Please help me i would really appreciate it, worth 11 points
Answers
The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.
How to Evaluate a Function?We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:
h(t) = 0 (height of the ground is 0)t = seconds the waste takes to height the groundInitial height = 400 feetPlug in the values into the equation of the function
0 = -16t² + 400
Solve for t
0 - 400 = -16t²
-400 = -16t²
-400/-16 = t²
400/16 = t²
√(400/16) = t
20/4 = t
5 = t
t = 5
The number of seconds it takes is: 5 seconds.
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Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates of A′ of the rotated quadrilateral A′B′C′D′?
Answers
A
3. What mathematical symbol is appropriate to use given the
word?
4. What word is appropriate to use given the symbol?
Answers
Answer:
X
Step-by-step explanation:
Mike has 63 toys. 18 of them are new and 12 are his favorites, while 4 are new and favorites. Mike is giving away all the toys that are neither new nor favorites. How many toys does mike have? ASAp
Answers
Answer:34
Step-by-step explanation:
Giving away all that is not new or fav so 12 fav + 18 new + 4 which are new an favorite = 34
Answer:
22
Step-by-step explanation:
63 is the total
14 are new
8 are fav
14+8=22
Three friends go to a store to rent games and movies. Calvin rents 3 movies and 2 video games and spends a total of $25. Samantha rents 2 movies and 1 video game and spends a total of $14.75.
If the rental fee for each game is the same and the rental fee for each movie is the same, determine how much their friend, Keith, will spend at the rental store to rent 1 movie and 2 video games. Explain your answer.
Answers
The Keith will spend $16 to rent 1 movie and 2 video games from the store.
How to solve the equation of two variable?Let's assume the rental fee for each movie is "m" and the rental fee for each game is "g".
From the given information, we can form the following system of equations:
3m + 2g = 25 (Calvin's rental)
2m + g = 14.75 (Samantha's rental)
We can solve for "m" and "g" by using elimination or substitution method. Here, we will use substitution method.
From the second equation, we can solve for "g" in terms of "m":
g = 14.75 - 2m
Substituting this into the first equation, we get:
3m + 2(14.75 - 2m) = 25
Simplifying this, we get:
3m + 29.5 - 4m = 25
-m + 29.5 = 25
-m = -4.5
m = 4.5
Now that we know the rental fee for each movie is $4.50, we can find the rental fee for each game by substituting "m" into either of the original equations:
2(4.5) + g = 14.75
g = 14.75 - 9 = 5.75
So the rental fee for each game is $5.75.
To find how much Keith will spend to rent 1 movie and 2 video games, we can simply add up the rental fees:
1(4.5) + 2(5.75) = 16
Therefore, Keith will spend $16 to rent 1 movie and 2 video games from the store.
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Solve 2( 32x-5) -4 =11
Answers
64x -10 -4 =11
Combine like terms
64x -14 =11
Add 14 to both sides
64x = 25
Divide by 64
X= 0.390625
The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet. Which represents the two-dimensional net of this pyramid?
Answers
The two-dimensional net of this pyramid that is surface area will be 34,416 square feet.
What is the surface area of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
The surface area of the pyramid will be
SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)
The largest pyramid at Giza is a square pyramid. It has a base of 756 feet and a slant height of 612 feet.
We have
L = W = 27.5 feet
Then the two-dimensional net of this pyramid that is surface area will be
SA = 2(1/2 × B × K) + 2(1/2 × L × K) + (L × B)
SA = 4(1/2 × 27.5 × 612) + 756
SA = 33,660 + 756
SA = 34,416 square feet
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Which of the following is equivalent to the expression?
Answers
Answer:
d
Step-by-step explanation:
- 5 (3x - 7) ← multiply each term in the parenthesis by - 5
= - 15x + 35
Answer: d.) -15x + 35
Given expression:
⇒ -5(3x - 7)
Apply distributive method: a(b + c) = ab + ac
⇒ -5(3x) -5(-7)
multiply the variables
⇒ -15x + 35
What is the relationship between \blueD{\angle a}∠astart color #11accd, angle, a, end color #11accd and \greenD{\angle b}∠bstart color #1fab54, angle, b, end color #1fab54?
Answers
Answer:
C
Step-by-step explanation:
supplementary because it adds to 180
Answer:C
Step-by-step explanation:
khan
The circumference of a circle is 19 ft.
What is the area, in square feet? Express
your answer in terms of T.
Answers
Answer:
The area is approximately 28.73ft²
Step-by-step explanation:
Given: Circumference = 19 ft
The necessary formula area,
Area: A = πr²
Circumference: C = 2πr
Combine:
A = [tex]\frac{C^{2} }{4\pi }[/tex]
A = [tex]\frac{19^{2} }{4\pi } \\\\ \frac{361 }{4\pi }[/tex]
A = 28.72747
3. Choose the equation that correctly shows the Commutative Property of Multiplication. 5 × 1 3 = 1 3 ÷ 5 5 × 1 3 = 5 × 1 3 5 + 1 3 = 1 3 × 5
Answers
According to the commutative property of multiplication, changing the order of components has no effect on the product. The correct option is B.
What is the commutative property of multiplication?According to the commutative property of multiplication, changing the order of components has no effect on the product.
For example: 4 × 8 = 8 × 4 = 32
The equation that correctly shows the Commutative Property of Multiplication is,
5 × 1 3 = 5 × 1 3
Hence, the correct option is B.
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