The base of the triangle is 15 meters.
Here, we are given that the height of a triangle is 5 m longer than the base.
Let the height of the triangle be h
Then, the base of the triangle will be = h - 5
Further, we are given that area of the triangle = 150 meter square
We know that area of a triangle = 1/2 × base × height
⇒ 150 = 1/2 × h × (h-5)
150 × 2 = h(h-5)
300 = [tex]h^{2}[/tex] - 5h
[tex]h^{2}[/tex] - 5h - 300 = 0
Now, we solve the above quadratic equation by splitting the middle term.
[tex]h^{2}[/tex] + 15h - 20h - 300 = 0
h( h + 15) - 20( h + 15) = 0
(h - 20) (h + 15) = 0
Thus, h = 20 or -15
But since height cannot be negative, h = 20
⇒ base = h - 5
= 20 - 5
= 15 meters
Thus, the base of the triangle is 15 meters.
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PLEASE HELP ME I NEED HELP ON MATH
Answer: THERE ARE NO RESTRIcTIONS
Step-by-step explanation: X cancels out every number
One leg of a right triangle is 7 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
Answer: 12
is the rounded answer using the Pythagoras theorum.
:) hope it's right:)
Step-by-step explanation:
Can i get help on this answer pls. 20 points rewarded for correct answer
Answer: (a) It appears to take the same amount of time to serve each customer. Predicted amount of time to serve 9 customers: 27
(b) Each dollar spent appears to earn the same number of points. 80 points : $8
I need help. 10 point for whoever can help.
Answer:
B=4
Hope that helps! :)
HELP I DONT KNOW HOW TO DO THIS
Answer:
Square root of 45
Step-by-step explanation:
Using pythagoras theorem:
6^2+3^2 = 36+9 = 45
which is [tex]\sqrt{45}[/tex]
There are 15 girls in your class this year. That is a 15% increase from last year. Write a proportion to solve for the number of girls in the class last year.
First, we have to recognize that if the current number of girls in the class is a 15% increase from last year, then this year's number is 115% of last year's number.
With that, we can set up a proportion comparing last year to this year, in both percentages and numbers:
[tex]\dfrac{100}{115} = \dfrac{x}{15}[/tex]
Note that both numerators are last year's values and the denominators are this year's values.
If we multiply both sides by 15, we have that x ≈ 13.043478260869565. Since we're dealing with whole people, we'd say that there were 13 girls in the class last year.
Use the commutative property to write an equivalent expression to 4g + 13, and show that they are equivalent for g =
10 and g = 2. Complete the statements.
If you change the order of the terms you can create the equivalent expression
and
After substituting 10 for g, the expressions are
After substituting 2 for g, the expressions are 4(2) + 13 and 13 + 4(2).
The expressions are equivalent because they both have a value of
when g = 2.
when g = 10 and a value of
The equivalent expression by commutative property is,
4g + 13 = 13 + 4g
Commutative property :
According to the commutative property, the numbers we use can be moved around or switched around without changing the result.
a +b =b+a
The given expression is 4g +13
The equivalent expression by the commutative property is
4g +13 = 13 +4g
For g = 10,
4(10) + 13 = 13 + 4(10)
40 +13 = 13 +40
53 = 53
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An object of mass 30 kg is in free fall in a vacuum where there is no air resistance. Determine
the acceleration of the object.
Answer:
a= g=9.81 m/s square
Mass given to us = 30 kg
Therefore we have to find the acceleration of the object,
As there is no air and mass is irrelevant in free fall, the acceleration the object experiences will be equal to the force of gravity. On our planet, the gravitational pull on an item falling there is approximately:
9.81 m/s square.
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in a test for particular illness, a false-positive result is obtained about 1 in 125 times the test is administered. if the test is administered to 15000 people, obtain the approximate probability of there being more than 135 false-positive results?
The probability of being more than 135 false-positive result is equal to 0.0853.
As given in the question,
Probability of false positive 'p' = 1/125
= 0.008
Number of people tested 'sample size n' = 15,000
Mean 'μ' = np
= 15000 × 0.008
= 120
Standard deviation 'σ' = √n × p × ( 1 - p )
= √15000 × 0.008 × ( 1 - 0.008)
=√ 15000 × 0.008 × 0.992
= √119.04
= 10.9
z = (X - μ) /σ
Approximate probability of being more than 135 false-positive results
= P( X > 135)
= P[( X - μ )/σ > ( 135 - μ)/σ
= P ( z > (135 - 120)/ 10.9)
= P ( z > 1.37)
= 1 - P ( z ≤ 1.37)
= 1 - 0.9147
= 0.0853 ( from z table)
Therefore, probability of being more than 135 false-positive results is equal to 0.0853.
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the probability distribution for the number of goals the lions soccer team makes per game is given below. number of goalsprobability 00.15 10.10 20.10 30.30 40.35 what is the probability that in a given game the lions will score less than 2 goals? a. 0.25 b. 0.35 c. 0.10
Answer:
0.35 because above all the probs were below 50 meaning that it was hard for them to even score one goal per game
Step-by-step explanation:
hi help me pls help help
Step-by-step explanation:
many greetings to your teacher, there are some definitions missing.
this can only be done if JM and LH are true diameters of the circle.
1. if LH is a diameter, then angles KAH + LAK = 180°.
KAH = 90° (right angle).
so,
angle LAK = 180 - 90 = 90°.
2.
with JM and LH being diameters, JAH = LAM = 42°.
JAH + JAK = 90°.
angle JAK = 90 - 42 = 48°.
3. angle LAJ = LAK + JAK = 90 + 48 = 138°.
4. see also 2.
these are angles of intersecting lines (diameters). they must be the same on both sides of such an intersected line (just left-right mirrored).
JAH = LAM = 42°.
5. angle KAM = LAK + LAM = 90 + 42 = 132°.
6. arc angle LK = angle LAK = 90°.
7. arc angle JK = angle JAK = 48°.
8. arc angle LMG = angle LAG = 180 - HAG =
= 180 - 30 = 150°.
9. arc angle JH = angle JAH = 42°.
10. arc angle KLM = angle KAM = 132°.
A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians?.
Its phase is 60 degrees and π/3 radian
From the question, we have
Each complete cycle measures 360 degrees.
So, 1/6 cycle = 1/6 × 360° = 60°
Each complete cycle measures 2π radian.
So, 1/6 cycle = 1/6 × 2π = π/3 radian
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. One of the basic mathematical operations is one that we commonly perform. The most obvious example is using multiplication tables. Mathematicians multiply two integers to illustrate the process of repeatedly adding one number to another. The types of numbers that can be included include natural numbers, fractions, integers, whole numbers, and others. When M is multiplied by n, it either adds or subtracts from itself 'n' times.
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4
The ratio of words
missed to correct B
on Marcy's spelling
test was 1:4. If she
got 4 words wrong,
how many were
correct?
A
6.RP.1: Ratio Concepts
C
D
4
8
16
20
Marcy got only 1 correct answer.
What is ratio?The relationship in quantity, amount, or size between two or more things in proportion.
Given that, the ratio of words corrects to wrong is 1:4
She got 4 wrong answers so, her correct answers count = 1
Hence, the Marcy answered only one correct answer.
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A rental car company charge $37. 93 per day to rent a car and $0. 11 for every mile driven. Taylor want to rent a car, knowing that:
She plan to drive 50 mile. She ha at mot $300 to pend. Which inequality can be ued to determine
d
d, the maximum number of day Taylor can afford to rent for while taying within her budget?
The inequality that can be used to determine the maximum number of days, d, Taylor can afford to rent for while staying within her budget is $37. 93(d) + $0. 11(50) < $300 or d < 7.76.
Inequality is defined as the relationship between non-equal numbers or expressions separated by <, >, ≤, or ≥.
Let d be the maximum number of days Taylor can afford to rent for while staying within her budget.
If a rental car company charges $37. 93 per day to rent a car and $0. 11 for every mile driven, and Taylor plans to drive 50 miles, then it will cost her $37. 93(d) + $0. 11(50).
If she has $300 at most to spend, then the inequality should be d < 7.76
$37. 93(d) + $0. 11(50) < $300
37. 93d + 5.5 < 300
37. 93d < 294.5
d < 7.76
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Charmaine worked 27 hours last month and earned $9 per hour. She spent $19 of her earnings since then. How much money does she have left?
Answer:
224
Step-by-step explanation:
(27x9) - 19
243 - 19 = 224
he shoe sizes of a group of middle school girls are shown.
5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
If a shoe size of 6 is added to the data, how does the IQR change?
The IQR becomes a 1.5.
The IQR remains a 2.
The IQR remains a 2.5.
The IQR becomes a 3.
If a shoe size of 6 is added to the data, there wouldn't be any change in the IQR. Therefore, the correct answer option is: B. the IQR remains a 2.
What is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁
Based on the given data set, the following interquartile ranges was calculated by using Microsoft Excel:
Q₃ = 8Q₁ = 6Now, the interquartile range (IQR) is given by:
IQR = Q₃ - Q₁
IQR = 8 - 2
IQR = 2
Adding a shoe size of 6 to the data set, the first and third and interquartile ranges remained the same, which implies that the interquartile range (IQR) would remain as two (2).
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Answer: The IQR stays the same therefor the option is "the IQR remains a 2."
Step-by-step explanation:
A triangle has vertices on a coordinate grid at A(-7, 5), B(8,5), and C(8,0).
What is the length, in units, of AB?a
Petra eats five and three-fifths pies in a pie-eating contest. Paulie eats three and fourteen-fifteenths pies in the contest. How many more pies did Petra eat?
two and five-tenths pies
two and ten-fifteenths pies
one and five-tenths pies
one and ten-fifteenths pies
Answer: 6 8/15
Step-by-step explanation:
What is 17.01 x 0.12?
Answer: 0.8412
Step-by-step explanation:
Please help I need help with both questions fast
zoom in
5. Does the graph represent a function?
ОО
Yes
No
*REQUIRED
*REQUIRED
6. Explain why the graph is or is not a
function below.
Type response
Answer:
Below
Step-by-step explanation:
YES function because there is only ONE value of Y for each value of X
Three eighths of the 48 roses were red. (a) How many roses were red? (b) How many roses were not red? (c) What fraction of the roses were not red?
Answer:
A. 18 roses were red.
B. 30 roses were not red.
C. 5/8 were not red.
Step-by-step explanation:
In order to do this question, we first need a calculator. Then, we take three eighths and divide them on the calculator to get:
3 divided by 8 = 0.375.
Then, on the calculator again, we take the 48 roses and find the percentage of the roses that were red, by multiplying it by 0.375:
0.375 x 48 = 18.
A. 18 roses were red.
Now, for the next question, how many roses were not red. We take the 48 roses and subtract it from the roses that were red, which were 18 roses:
48 - 18 = 30.
B. 30 roses were not red.
Now, to find the fraction of the roses that weren't red. We take the 30 roses that weren't red and divide it by the total amount of 48 roses:
30 divided by 48 = 0.625.
In order to make 0.625 into a fraction, we take the higher, but lowest 100th place we can make for 0.625:
625/1,000.
Now, we simplify it:
625 divided by 5 = 125
1,000 divided by 5 = 200
Now, we have 125/200.
Simplify more:
125 divided by 5 = 25
200 divided by 5 = 40
Once more:
25 divided by 5 = 5
40 divided by 5 = 8
Our final fraction is 5/8.
C. The fraction of the roses that were not red are 5/8.
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What is the amount of error that you will accept in the upper tail of the confidence interval?.
The amount of error that you will accept in the upper tail of the confidence interval as follows
The amount of error that will accept in the upper tail is = 13.97
Amount of error = margin of error
Margin of error = [tex]Z\frac{\alpha }{2} \frac{s}{\sqrt{n} }[/tex]
93% = confidence interval =1- [tex]\alpha[/tex]
=1-.93
=0.07
Hence [tex]\frac{\alpha }{2}[/tex] =0.035
[tex]Z\frac{\alpha }{2} or t\frac{\alpha }{2} = 1.81[/tex]
This problem represents two tail test because a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
And confidence interval are always two tailed.
So margin of error = [tex]1.81x\frac{1.99}{\sqrt{40} }[/tex]
= 0.57
Upper tail C.I = x + margin of error
=13.4+0.57
=13.97
Lower tail C.I = x - margin of error
= 13.4 - 0.57
=12.83
Hence the answer is, the amount of error that will accept in the upper tail is = 13.97.
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Emily made 8 field goals in 25 attempts. What decimal represents the number of field goals she made?.
The decimal form of the number of filed goals Emily made is 0.32
Total number of attempts Emily made = 25
Total number of field goals = 8
We need to represent the filed goals in decimal
What is decimal?
A decimal is a number that includes a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
feild goals is 8 out of 25
so, it is 8/25
= 0.32
Therefore, the decimal form of the number of filed goals Emily made is 0.32
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A fair coin can only land on heads or tails with equal probability.
What is the probability it lands on tails?
Answer: 50% ion know
Step-by-step explanation: its half and half sorry im st*pid
WILL GIVE BRAINLIEST!!!
Why does the square root of 9 equal both 3 and -3?
Answer:
See below
Step-by-step explanation:
3 * 3 = 9 obviously
a negative number times a negative number equals a positive number
so -3 * -3 = + 9
I need help right away now ??!??!
The expected value is 11.134
The expected value can be calculated as:
EV = ∑xₙ*pₙ
Where xₙ is the n-th outcome. For the case of the spinner we have 2 possible outcomes:
x₁ = 9
x₂ = 4
And pₙ is the probability of the n-th event.
For the case of each spinner, the probability of each section will be equal to the quotient between the degrees of each arc, and the total number of degrees in a circle (360°).
First, we can see that for outcome = 9, the angle is a right angle, then it is equal to 30°, then the probability of this event will be:
p₁ = 30°/360° = 0.083
And the angle for the second arc must be such that:
30 + A = 360°
A = 360 - 30 = 330
Then the probability for the outcome = 4 is:
p₂ = (330°/360°) = 0.916
Now we can find the expected value as:
EV = (*9 x 0.083 + 4 x 0.916 ) = 11.134
Therefore, the expected value is 11.134
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can someone help find the volume
Answer:
the first one 792 ft²
Step-by-step explanation:
you do length times width times height = lxwxh
A cars company sells require a down payment of $2000 and 48 monthly payments. The contract amount for any of the cars is at least $19,940. What is the amount of the monthly payment? (To the nearest whole dollar) as an inequality?
Answer:923.36
Step-by-step explanation:
20
Write "less" or "greater" in the blank.
304 is than 340
Answer:less than
Step-by-step explanation:304 is a smaller number than 340
Can the equation x² = 10 be solved by factoring?
Solve it x = +/-
The required simplified solution of the given expression is given as ±√10.
Given that,
To determine the simplified solution of x² = 10, by factorization.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
x² = 10
Taking square root on both sides,
x = ±√10
Thus, the required simplified solution of the given expression is given as ±√10.
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