Answer:
Division property of equality.
Marlon built a ramp to put in front of the curb near his driveway so he could get to the sidewalk more easily from the street on his bike. A rectangular prism with a length of 6 inches, width of 18 inches, and height of 6 inches. A triangular prism. The triangular sides have a base of 8 inches and height of 6 inches. The prism has a height of 18 inches. If the ramp includes the flat piece as well as the angled piece and is made entirely out of concrete, what is the total amount of concrete in the ramp? 768 inches cubed 936 inches cubed 984 inches cubed 1,080 inches cubed
Answer: 1,080 in. cubed
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Teresa is investigating if grade level has any effect on time spent studying. What is the response variable?
Answer:
The time spent studying is the response variable.
Step-by-step explanation:
The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable. In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.
The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.
A right triangle has two shorter sides that differ in length by 7cm. The length of the
hypotenuse is 8 cm longer than the shortest side. Find the lengths of the three sides.
Show all of your steps.
Pls help!!! 75 points
Answer:
a = 5
b = 12
c = 13
Step-by-step explanation:
a^2+b^2=c^2
b-a=7(b=a+7)
c=a+8
Then, substitute
a^2+((a+7)*(a+7))=c^2
a^2+a^2+7a+7a+49=c^2
2a^2+14a+49=c^2
Because c = a+8
2a^2+14a+49=(a+8)(a+8)
2a^2+14a+49=a^2+16a+64
a^2-2a=15
a^2-2a-15=0
(a-5)(a+3)=0
a = 5,-3
a = 5(a side cannot be negative)
Plug in a=5 to the other equations to get
a = 5, b = 12, c = 13
Hope it helps <3
Answer:
The lengths of the sides are 5, 12, 13.
Step-by-step explanation:
In a right triangle, the two shorter sides are the legs. The longest side is the hypotenuse.
Let the shorter leg = x.
The longer leg is 7 cm longer, so its length is x + 7.
The length of the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8.
The lengths are:
x, x + 7, x + 8
Since the triangle is a right triangle, we can use the Pythagorean theorem.
a^2 + b^2 = c^2
x^2 + (x + 7)^2 = (x + 8)^2
Square the trinomials.
x^2 + x^2 + 14x + 49 = x^2 + 16x + 64
Combine like terms and place them all on the left side equaling zero.
x^2 - 2x - 15 = 0
Factor the left side.
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Since the length of a side of a triangle cannot be negative, we discard the solution x = -3.
x = 5
x + 7 = 5 + 7 = 12
x + 8 = 5 + 8 = 13
Answer: The lengths of the sides are 5, 12, 13.
Draw a graph of f(x) =3^-x+3
Answer:
Use a graphing calc or desmos
Step-by-step explanation:
Phoenix hiked the Rocky Path Trail last week. It took four days to complete the trip. The first two days she hiked a total of 26 miles. The second and third days she averaged 12 miles per day. The last two days she hiked a total of 28 miles. The total hike for the first and third days was 22 miles. How many miles long was the trail?
Answer:
50 miles
Step-by-step explanation:
let he hiked a,b,c and d miles on each of the four days respectively.
then, according to the question.
a+b=26...i
b+c= 24...ii
c+d=28...iii
a+c=22...iv
now, adding i,ii,iii,iv we get
2(a+b+c+d) = 100
a+b+c+d= 50 miles.
Hence, he traveled in all 50 miles.
Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. Denote this by H (the remaining were away games). Of all the games, 25% were wins. Denote this by W (the remaining were losses). Of all the games, 20% were at-home wins. Of the at-home games, we are interested in finding what proportion were wins. Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins?A. P(H)B. P(W)C. P(H and W)D. P(H | W)E. P(W | H)
Answer:
E. P(W | H)
Step-by-step explanation:
What each of these probabilities mean:
P(H): Probability of the game being at home
P(W): Probability of the game being a win.
P(H and W): Probability of the game being at home and being a win.
P(H|W): Probability of a win being at home.
P(W|H): Probability of winning a home game.
Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins?
This is the probability of winning a home game. So the answer is:
E. P(W | H)
What is the measure of C?
Answer:
C.) 60°
Step-by-step explanation:
The triangle is an equilateral triangle. So that means that all the angles measure the same. And we have to remember that a triangle always equals 180°
So, to find out the measure of an angle. We must divide 180 by 3. Which is 60
=60°
Hope this helps you out! : )
what is the length of ac? a)96 b)132 c)72 d)136
Answer:
show a picture
Step-by-step explanation:
What is the slope of the line between (−4, 4) and (−1, −2)?
Answer:
-2
Step-by-step explanation:
The slope of a line is
m = (y2-y1)/(x2-x1)
= (-2 -4)/(-1 - -4)
= -6/ ( -1 +4)
= -6 /3
=-2
Answer:
[tex]= - 2 \\ [/tex]
Step-by-step explanation:
[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]
Now let's find the slope
[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]
hope this helps you.
brainliest appreciated
good luck! have a nice day!
PLEASE HELP!!!!!! Find common difference
Answer:
d = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference , thus
a₇ = a₁ + 6d
a₄ = a₁ + 3d
Given a₇ - 2a₄ = 1 , then
a₁ + 6d - 2(a₁ + 3d) = 1, that is
a₁ + 6d - 2a₁ - 6d = 1
- a₁ = 1 ( multiply both sides by - 1 )
a₁ = - 1
Given a₃ = 0 , then
a₁ + 2d = 0 , thus
- 1 + 2d = 0 ( add 1 to both sides )
2d = 1 ( divide both sides by 2 )
d = [tex]\frac{1}{2}[/tex]
Solve 56000(1+1.8%)^5
Answer:
The solution to this expression is 61,224.74
Step-by-step explanation:
To solve we initially have to convert the percentage to a decimal:
[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]
So
56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74
The solution to this expression is 61,224.74
You and 3 of your friends decide to sell lemonade around town, and then split the money you make evenly. You decide to sell each cup of lemonade for 50 cents. In total, you all sell 120 cups of lemonade. How much money will each of you earn? Write an expression for the problem too.
Expression:
Answer:
$15
Step-by-step explanation:
Each cup is 50 cents which is basically $0.50
Multiply $0.50 by 120= $60
Because you and your three friends equal 4 total people,
divide 60 by 4 to get your own profit:
60/4=15
Translate the following arguments into symbolic form. Then determine whether each is valid or invalid by constructing a truth table for each.If microchips are made from diamond wafers, then computers will generate less heat. Computers will not generate less heat and microchips will be made from diamond wafers. Therefore, synthetic diamonds will be used for jewelry.
Answer:
Argument is valid.
Step-by-step explanation:
Let M, C and S represent the premises. The the statements can be represented using these letters as:
M: Microchips are made from diamond wafers.
C: Computers will generate less heat.
S: Synthetic diamonds will be used for jewelry.
1st premises:
If microchips are made from diamond wafers, then computers will generate less heat.
Notice that the above statement is a conditional statement. So to represent such relationship, the material implication is used which has ⊃ symbol.
This can be translated into symbolic form using the horseshoe operator ⊃ as:
M ⊃ C
2nd premises:
Computers will not generate less heat and microchips will be made from diamond wafers.
Notice that the above statement is a compound statement. It has two part joined together with "and" i.e. Computers will not generate less heat "and" microchips will be made from diamond wafers. These are two conjuncts and both should be true for the premises/compound statement to be true. So to represent such relationship, the Conjunction is used which has • symbol.
This can be translated into symbolic form using the dot • symbol as:
Computer will not generate less heat is represented as ~C because C states that Computer will generate less heat and ~C states that Computer will not generate less heat. So ~C is the negation of C. Now the complete symbolic form is:
~C • M
third premises:
Therefore, synthetic diamonds will be used for jewelry is represented as:
S
This is basically the conclusion statement.
Truth Tables:
For M:
M
T
T
T
T
F
F
F
F
For C:
C
T
T
F
F
T
T
F
F
For ~C:
It reverses the truth values of C
~C
F
F
T
T
F
F
T
T
For S:
S
T
F
T
F
T
F
T
F
For M ⊃ C:
The above mentioned premise formed with this connective is true unless the left the antecedent is true and right the consequent is false.
M C M ⊃ C
T T T
T T T
T F F
T F F
F T T
F T T
F F T
F F T
For ~C • M
The truth table of conjunction of ~C and M is formed using truth table of reverse of C i.e. ~C and that of M. The conjunction is true when both conjuncts are true and if either of the two conjuncts is false then whole conjunction is false.
M ~C ~C • M
T F F
T F F
T T T
T T T
F F F
F F F
F T F
F T F
Now combining all to check the validity:
M C S M ⊃ C ~C • M S
T T T T F T
T T F T F F
T F T F T T
T F F F T F
F T T T F T
F T F T F F
F F T T F T
F F F T F F
The given argument is valid. The is because it is impossible for the above premises to be true and the conclusion to be false. You can see that when the premises M ⊃ C and ~C • M are true the conclusion S is also true.
We check validity by checking in the truth table if there is a row that has all true premises and a false conclusion. If there is then argument is invalid. Here in the truth table you can see that no row has all the premises true and a false conclusion. So the argument is valid.
Plz help and have a correct answer! everyone is wrong...will mark brainliest!
Answer:
11) The intersection of two sets is the set of the elements that are common for both sets, in this case, we can see that: 79, 83 and 99 appear in both sets, then the intersection is: {79, 83, 99}
12) the union of both sets (all the possible options in the selection) is:
{75, 79, 82, 83, 94, 99, 101, 105} and the intersection set is {79, 83, 99}
So we have 8 elements in total, and 3 of them belong to the intersection, then the probability of selecting at random one element that belongs in the intersection is:
p = 3/8 = 0.375
13) In this case, the universal set is the set of all the real numbers.
You can remember that the set of all real numbers is equal to the union of the sets of the rational numbers and the set of the irrational numbers (and those two sets do not share any element).
Then, if we have only the set A = set of the irrational numbers, the complement will be the set of the rational numbers, because we must have that:
Set A U complement = Real set = irrational U rational.
(where U stands for "union")
now we replace Set A = irrational.
Irrational U complement = irrational U rational
complement = rational.
Let g be the function defined by g(x) = − 1 2 x + 5 if x < 6 x − 6 if x ≥ 6. Find g(−6), g(0), g(6), and g(12). g(−6) = g(0) = g(6) = g(12) =
Answer:
g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6
Step-by-step explanation:
We assume your function definition is ...
[tex]g(x)=\left\{\begin{array}{ccc}-\dfrac{1}{2}x+5&\text{for}&x<6\\x-6&\text{for}&x\ge 6\end{array}\right.[/tex]
For each given value of x, determine which segment applies, then evaluate.
For x = -6 and for x = 0, the first segment applies:
g(-6) = (-1/2)(-6) +5 = 3 +5 = 8
g(0) = (-1/2)(0) +5 = 5
For x = 6 and x = 12, the second segment applies:
g(6) = (6) -6 = 0
g(12) = (12) -6 = 6
In summary, ...
g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6
Pleaseeeeeee helppppppp
Answer:
[tex]\boxed{Option \ D}[/tex]
Step-by-step explanation:
The combination of a rational number (3) and an irrational no. ([tex]4i[/tex]) is called a complex number.
So,
[tex]3+4i[/tex] is a complex no.
Answer:
D. Complex number.
Step-by-step explanation:
This number is not irrational, since 3 is rational.
The number is not entirely rational, since 4i is irrational.
The number is not real because i is not real.
So, the number is a Complex number, since it includes both real and nonreal numbers.
Hope this helps!
Follow the directions to solve the system of equations by elimination. 8x + 7y = 39 4x – 14y = –68 Multiply the first equation to enable the elimination of the y-term. Add the equations to eliminate the y-terms. Solve the new equation for the x-value. Substitute the x-value back into either original equation to find the y-value. Check the solution.
Answer:
x=½
y=5
Step-by-step explanation:
(8x+7y=39)2
16x+14y=78
4x-14y=-68 add the two equations
20x=10.
divide both sides by 20
x=½
8x+7y=39
4+7y=39
7y=39-4
7y=35
y=5
The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.
8x + 7y = 39
4x – 14y = –68
Multiply the first equation to enable the elimination of the y-term:Multiply by 2
16x + 14y = 78
Add the equations to eliminate the y-terms:-14y + 14y = 0
4x + 16x = 20x
-68 + 78 = 10
Solve the new equation for the x-value20x = 10
x = 1 / 2
Substitute the x-value back into either original equation to find the y-value8(1 / 2) + 7y = 39
4 + 7y = 39
7y = 35
y = 35 / 7
y = 5
learn more on system of equation here: https://brainly.com/question/3861421?referrer=searchResults
3. What is the explicit formula for the arithmetic sequence 2, 7, 12, 17, ...?
Step-by-step explanation:
The given sequences are;
2,7,12,17......
difference =5
by using formula,
we get,
tn=a+(n-1)d
tn= 2+(n-1)5
Therefore, tn is 5n-3 is required formula for this arithmetic sequences.
Hope it helps....
Elif is arranging 28 chairs in rows in a room. Each row must be the same
length. The room is wide enough to make a row of 9 chairs, but no more
The room is deep enough to make 8 rows, but no more. What are the
possible numbers of rows and chairs in each row that Elif can make?
Answer:
Hey there!
Elif can only arrange the chairs like: 4 by 7, and 7 by 4.
Hope this helps :)
In a 2-card hand, what is the probability of holding only face cards?
Answer:
12
Step-by-step explanation:
( J , Q, K 4 each)
so prob that for 2 cards, both cards are face
= C(12,2)/C(52,2) = 66/1326 = 11/221
There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total nu
present. Express as a simplified ratio.
03:4
03:7
O 7:3
O 4:3
Answer: B) 3:7
Step-by-step explanation:
104/78 = .75
so for everyone 3 males there are 4 females,
then for every 7 people there are 3 males so the answer is B
<!> Brainliest is appreciated! <!>
The ratio between the males and the total number of persons will be 03:7
What is a ratio?It is a kind of relationship between two variables. It represents the weightage of one variable in comparison to other.
How to find the ratio?Number of males present=78
Number of females present=104
Total number of people present=182
Ratio=number of males: number of people
=78:182=39:91=3:7
Hence the ratio of males to total people is 3:7
Learn more about ratio at https://brainly.com/question/2328454
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Use x=1 to identify the value of each expression.
Answer:
[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]
The public radio show "A Prairie Home Companion," features news from the fictional town of Lake Wobegon, MN, home to many Norwegian bachelor farmers, and where "all the women are strong, all the men are good looking, and all the children are above average." Suppose average means average for the town. Such a town could not possibly exist, because (select all that apply)
a. not all women are strong
b. not all the children can be above average
c. not all Norwegian bachelor farmers are good looking
d. half the children must be below average
Answer:
b. not all the children can be above average
d. half the children must be below average
Step-by-step explanation:
In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.
Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.
Therefore, the correct answers are:
b. not all the children can be above average
d. half the children must be below average
Answer:
Second and last options are correct choices.
Step-by-step explanation:
If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.
Best Regards!
If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 40
Answer:
1.79% probability that the number of times that the coin lands tails will be less than 40
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Fair coin:
Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]
100 times
[tex]n = 100[/tex]
Then
[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]
What is the probability that the number of times that the coin lands tails will be less than 40
Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39.5 - 50}{5}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
1.79% probability that the number of times that the coin lands tails will be less than 40
Select all numbers that are in the range.
-3
-2
-1
0
1
2
-2
0
2
Answered on edge
Answer:
-2, 0, 2
Step-by-step explanation:
edge 2020
What is the equation of the line ( -4,8 ) ( 0,0 )
Answer:
Step-by-step explanation:
First you need to find the slope of the line that contains those 2 points.
[tex]m=\frac{0-8}{0-(-4)}=\frac{-8}{4}=-2[/tex]
So the slope is -2. Now we can pick one of those points and sub it into the point-slope formula to find the equation:
y - 0 = -2(x - 0) gives us an equation of
y = -2x
what is the solution set of y= x^2+2x+7 and y= x+7 ?
Answer:
(-1, 6)
(0, 7)
Step-by-step explanation:
Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.
Find the radius of the cylinder when volume is 304 cm^3 and height is 10 cm
Answer:
3.11 cmsolution,
Volume of cylinder=304 cm^3
height=10 cm
Radius=?
Now,
[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]
Hope this helps..
Good luck on your assignment..
The confidence interval on estimating the heights of students is given as (5.4, 6.8). Find the sample mean of the confidence interval.
Answer:
The sample mean is 6.1
Step-by-step explanation:
Margin of Error (E) = (upper limit - lower limit)/2 = (6.8 - 5.4)/2 = 1.4/2 = 0.7
Sample mean = lower limit + E = 5.4 + 0.7 = 6.1
rounded to the nearest whole, what is the radius length if minor arcYZ = 12 and angleYXZ is one-third of a full circle? (i guessed it idk if it’s right)
Answer:
Option (1)
Step-by-step explanation:
Since the length of arc YZ = 12 units
m∠YXZ = one third of the full circle = [tex]\frac{360}{3}[/tex] = 120°
From the formula of arc length,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = Central angle subtended by the arc
r = radius of the circle
By substituting these values in the formula,
12 = [tex]\frac{120}{360}(2\pi r)[/tex]
12 = [tex]\frac{2}{3}\pi r[/tex]
[tex]18=\pi r[/tex]
r = [tex]\frac{18}{\pi }[/tex]
r = 5.73
r ≈ 6 units
Therefore, Option (1) will be the answer.