Answer:
7 x 4
Step-by-step explanation:
Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7
If two events, A and B, never occur at the same time they are _____.
complementary
compound
simple
disjoint
Answer:
Disjoint is the correct answer.
Find the number that comes after 144five
Answer:
The number that comes after 144five is:
= 200five.
Step-by-step explanation:
Adding 1 to 144 base 5 will result in:
144
+ 1
= 200
b) To obtain the next number that comes after 144five, add 1five to 144five. Since the numbers are in base 5, 1five added to 4five will result in 0 with 1 carried backward. When 1 is added to the next 4, the result will be 0 with 1 carried backward. 1 added to 1 = 2, all in base 5. Figures in base 5 cannot exceed 4. The usual numbers for a base 5 operation are 0, 1, 2, 3, and 4.
The image is attached below. Thank you
Use the drawing tools to form the correct answer on the graph.
Plot function g on the graph
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
same as the person above plato 2022'
the measures of three angles of a triangle are given by (8x-10), (2x), and (3x-5). What is the measure of the larges tangle
9514 1404 393
Answer:
110°
Step-by-step explanation:
The sum of angles of a triangle is 180°.
(8x -10) +(2x) +(3x -5) = 180
13x -15 = 180
13x = 195
x = 15
The largest angle is ...
8x -10 = 8(15) -10 = 110 . . . . degrees
If the length of a leg of a right triangle is 25 and the length of the hypotenuse is 35, what's the length of the other leg, to the nearest tenth?
Answer:
24.5
Step-by-step explanation:
using Pythagorean theorem
[tex]a^{2} +b^{2} =c^{2} \\[/tex]
Since we know the hypotenuse, we can change up the theorem into [tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]35^{2} -25^{2} =a^{2}[/tex]
1225-625=[tex]a^{2}[/tex]
[tex]\sqrt{a^{2} } =24.5[/tex]
The sum of two integers is 90 and their difference is 30. Find the larger number
Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15.
(a) Find the IQ scores that represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
(c) Find the IQ score for the top 5%.
Answer:
a) IQ scores of 94.2 and below represent the bottom 35%.
b) An IQ score of 110.1 represents the 3rd quartile.
c) IQ scores of 124.7 and higher are in the top 5%.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
(a) Find the IQ scores that represent the bottom 35%.
The 35th percentile and below, in which the 35th percentile is X when Z has a p-value of 0.35, so X when Z = -0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.385 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -0.385*15[/tex]
[tex]X = 94.2[/tex]
IQ scores of 94.2 and below represent the bottom 35%.
(b) Find the IQ score that represents the 3rd Quartile.
This is the 100*3/4 = 75th percentile, which is X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 0.675*15[/tex]
[tex]X = 110.1[/tex]
An IQ score of 110.1 represents the 3rd quartile.
(c) Find the IQ score for the top 5%.
IQ scores of at least the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.645*15[/tex]
[tex]X = 124.7[/tex]
IQ scores of 124.7 and higher are in the top 5%.
A pharmacist wants to make 36ml of a 65% hydrogen peroxide solution. how many pls of 75% hydrogen peroxide must he mix with 57% hydrogen peroxide to make the desired solution?
Answer:
16 mls of the 75% solution and 20 mls of the 0.57% solution.
Step-by-step explanation:
Set up a system of equations:
Let x = volume of 75% solution and y be volume of 57% solution
0.75x + 0.57y = 36*0.65
0.75x + 0.57y = 23.4.......(1)
x + y = 36.........(2)
From equation (2):
y = 36 - x
Substituting this into equation(1):
0.75x + (0.57(36 - x) = 23.4
0.75x + 20.52 - 0.57x = 23.4
0.18x = 23.40 - 20.52 = 2.88
x = 2.88/0.18
x = 16
so from equation (2): y = 36-16 = 20.
Which of the following is a geometric sequence where a1 = 4 and r = 3?
A) 4, 7, 10, 13, . . .
B) 3, 7, 11, 15, . . .
C) 4, 12, 36, 108, . . .
D) 3, 12, 48, 192, . . .
Answer:
C 4,12,36 108
Step-by-step explanation:
the answer is above.
Answer:
C
Step-by-step explanation:
G.P= a,ar,ar^2,ar^3,...,
a1=4
a2=4×3=12
a3=4×9=36
a4=4×27=108
A jar contains 11red marbles, 12 blue marbles and 6 white marbles. Four marbles from the jar are selected. With each marble being replaced after each selection. What is the probability that the first red marble chosen is on the 5th selection?
Answer:
Red on the 5th draw = 0.0907
Step-by-step explanation:
The first to fourth selections are all the same.
Blue + white = 12 + 6 = 18
The total number of marbles is 11 + 12 + 6 = 29
P(~ red) for the first four times = (18/29)^4 = 0,1484
Now on the 5th time, the first red is 11/18
So the Probability is 0.1484 * 11/18 = 0.0907
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
Leah is looking to take out a 30-year mortgage from a bank offering a monthly interest rate of 0.325% Using the formula below, determine the maximum amount Leah can borrow, to the nearest dollar, if the highest monthly payment she can afford is $900.
M=Pr/(1-(1+r)^-n)
M= the monthly payment
P= the amount owed
r= the interest rate per month
n= the number of payments
Answer:
[tex]P=\$276646.153[/tex]
Step-by-step explanation:
Time [tex]T=30years[/tex]
Rate [tex]r=0.325\%[/tex]
Payment per month [tex]P=\$ 900[/tex]
Generally the equation for Principle is mathematically given by
[tex]M=\frac{P r}{1-(1+r)^{-n}}[/tex]
[tex]900=\frac{P \frac{0.325}{100}}{1-(1+( \frac{0.325}{100}))^{- 30*12}}[/tex]
[tex]P=\frac{900*100*0.99}{0.325}[/tex]
[tex]P=\$276646.153[/tex]
moses is inviting 10 friends to a party each friend wants 4 cookies and each box has 10 cookies how many boxes should moses get?
Answer:
4
Step-by-step explanation:
Since each friend wants 4 cookies, and there are 10 friends, there are 10 x 4 = 40 cookies total Moses should buy. Since each cookie box has 10 cookies in it, he should buy 40/10 = 4 total cookie boxes.
Noah charges $20 for each lawn that he mows.
Answer:
m = 20 * n
Step-by-step explanation:
The money that he earns is equal the amount earned per lawn times the amount of lawns that he mows
m = 20 * n
Answer:
60 = 3 x 20
Step-by-step explanation:
60 = m
3 = c
20 = n
Let x represent the regular price of any book in the store. Write an expression that can be used to find the sale price of any book in the store.
Answer:
.
e
Step-by-step explanation:
.
I need help with this
Answer:
[see below]
Step-by-step explanation:
Reflection over the x axis is: [tex](x,y)\rightarrow(x,-y)[/tex]
(0, -2) - > (0, 2)
(5, -1) - > (5, 1)
(2, -4) - > (2, 4)
A'B'C' should be (0,2), (5,1) and (2,4). (Or option B)
Hope this helps.
solve each question please thank you
Answer:
SURE
Step-by-step explanation:
Find the intersection of the line and the circle given below
y=-x-3
x^2+y^2=17
Answer:
There are two points of intersection
(-4,1) and (1,-4)
Step-by-step explanation:
Answer:
the guy above me is correct
Step-by-step explanation:
Find the exact value of the logarithm without using a calculator.
Answer:
1/11
Step-by-step explanation:
We are asked to find the natural log of
[tex] \sqrt[11]{e} [/tex]
Convert to fractional exponent
[tex] ln(e {}^{ \frac{1}{11} } ) [/tex]
Apply Log of Power rule
[tex] \frac{1}{11} ln(e) [/tex]
Natural log of e is 1 so
[tex] \frac{1}{11} \times 1 = \frac{1}{11} [/tex]
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
First, remember that the ln function is just a log function with a base of e. Here's how it looks
[tex]ln(x) =log_{e}(x)[/tex]
[tex]ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )[/tex]
We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!
[tex]log_{e}(e^{\frac{1}{11} } )[/tex]
Solving the equation above is really simple. All that function is really saying is can we raise e to some number, where the result would be e^(1/11)? In other words find x.
[tex]e^{x} = e^{\frac{1}{11} }[/tex]
Well x has to be 1/11 in that case. And that ends up being our final answer.
[tex]log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}[/tex]
Find the missing side. Round your answer to the nearest
Please help me
Answer:
Step-by-step explanation:
PLEASE HELP QUICKLY
Determine whether the given sequence could be arithmetic. If so, identify the first difference and the next term.
-6, -11, -16, -21, -26.....
Answer:
The first difference is -5. The next term is -31.
Step-by-step explanation:
If you find the difference between -6 and -11, then you get -5.
And, all the other ones also have differences of -5, so basically, the next term is -31.
Thanks! Please mark me Brainliest!
Answer:
It could be arithmeticIf so, then the first difference is -5 and the next term is -31===================================================
Explanation:
Pick any term and subtract off the previous term
term2 - term1 = -11 - (-6) = -11 + 6 = -5term3 - term2 = -16 - (-11) = -16 + 11 = -5term4 - term3 = -21 - (-16) = -21 + 16 = -5term5 - term4 = -26 - (-21) = -26 + 21 = -5No matter what we picked, we end up with the same result which is -5. This is the common difference aka first difference.
If this pattern keeps up forever, then the sequence is arithmetic.
And if the pattern keeps up, then the next term would be
term6 = term5 + (common difference)
term6 = -26 + (-5)
term6 = -31
Note: Adding -5 is the same as subtracting 5.
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
Find the measure of each side of this triangles. Answer in exact form.
Answer:
[tex]sin(0)=opposite/hypotenuse,cos(0)=adjacent/hypotenuse[/tex]
[tex]sin(60)=\frac{x}{8\sqrt{5} } ,\:\:cos(60)=\frac{y}{8\sqrt{5} }[/tex]
[tex]\frac{\sqrt{3} }{2} =\frac{x}{8\sqrt{5} } \:\:\:\:\frac{1}{2} =\frac{y}{8\sqrt{15} }[/tex]
[tex]2x=8\sqrt{5} \times\sqrt{3} \:\;\:\:2y=1\times8\sqrt{15}[/tex]
[tex]2x=\frac{8\sqrt{15} }{2} \:\:\:\:2y=8\sqrt{15}[/tex]
[tex]x=8\sqrt{15} /2\:\:\: y=8\sqrt{15} /2[/tex]
[tex]x=4\sqrt{15}[/tex] [tex]y=4\sqrt{15}[/tex]
OAmalOHopeO
find find the equation of straight line find the equation of straight line joining the points 3 4 and 5 7
A runner is traveling at a constant rate of 8 meters per second. How long does it take for the runner to travel 100 meters? Now before you answer this I know it's 12.5! What I need help with is creating a equation that gives the distance, d, that the person has run if you know the amount of time, t, they have been running. Thank you! :)
Answer:
see below
Step-by-step explanation:
We know that distance = rate * time
100 meters = 8 m/s * time
100 = 8t
Divide each side by 8
100/8 = 8t/8
12.5 = t
If we know the rate and the time, we can find the distance
d = rt
Help me again? Thanks to whomever does! Please show work!
Answer: See Below
Step-by-step explanation:
Concept:
Here, we need to know the idea of alternative interior angle, alternative exterior angle, and corresponding angles.
Alternative interior angle: a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
Alternative exterior angle: a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
Corresponding angle: A pair of angles that occupy the same relative position at each intersection where a straight line crosses two others.
All three kinds of angles above occur to be congruent (equal) when the lines are parallel to each other.
If you are still confused, please refer to the attachment below for a graphical explanation
Solve:
PART ONE
a) Name two pairs of alternative exterior angles: ∠1 and ∠7 / ∠2 and ∠8
b) Name two pairs of corresponding angles: ∠1 and ∠5 / ∠2 and ∠6
c) Name two pairs of alternative interior angles: ∠4 and ∠6 / ∠3 and ∠5
PART TWO
a) If the measure of angle 7 is 52°, what is the measure of angle 1?
As we can see from above, ∠1 and ∠7 are alternative exterior angles. They are part of parallel lines, thus according to the properties, they are equal.m∠1 = m∠7 = 52°b) If the measure of angle 8 is 112°, then what is the measure of angle 3?
As we can see from the figure given, ∠8 and ∠7 are linear pairs or supplementary angles, which adds up to 180°.m∠7 = 180 - m∠8 = 180 - 112 = 68°As we can see from the figure given, ∠7 and ∠3 are corresponding angles.They are part of parallel lines, thus according to the properties, they are equal.m∠3 = m∠7 = 68°Hope this helps!! :)
Please let me know if you have any questions
What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
Mr. Plaggenier divided Camp Greenfield into 5 squads for an athletic scrimmages. Each squad competes against each of the other 4 squads 2 times. The scrimmage lasts 2 hours. If only one pair of teams competes at a time and all of the competitions take the same amount of time, how long is each competitions?
A)6 min.
B) 8 min.
C) 10 min.
D) 12 min.
Answer: (a)
Step-by-step explanation:
Given
There are 5 squads for an athletic scrimmages
If each team played 2 matches
Total no of matches will be
[tex]\Rightarrow \dfrac{5(5-1)}{2}\times 2=20\ \text{matches}[/tex]
So, 20 matches are played in 2 hours
Each match takes
[tex]\Rightarrow \dfrac{120}{20}=6\ \text{minute}[/tex]
Option (a) is correct.
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker
Discounted price = $60
Discount = 60%
Let the usual price be x.
So, x - (60% of x) = $60
=> x - [(60/100) × x] = $60
=> x - (60x/100) = $60
=> x - (3x/5) = $60
=> (5x/5) - (3x/5) = $60
=> 2x/5 = $60
=> 2x = $60 × 5
=> 2x = $300
=> x = $300/2
=> x = $150
So, the usual price is $150.
HELP
1) Determine the sum of row 19 in Pascal's triangle
Answer: 262144
Step-by-step explanation: You can calculate & draw it out. Then, add the values in the second-to-bottom row of the picture below.
262144 if I'm correct....
