The two numbers are 6 and 20 respectively.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that one number is 10 less than 5 times the second number. Their sum is 26.
Let the numbers be [x] and [y] repsectively. Then, we can write that -
x + y = 26 ..... Eq[1]
x = 5y - 10 ..... Eq[2]
We can write -
x + y = 26
5y - 10 + y = 26
6y = 36
y = 6
Then, we can write [x] as -
x = 5 x 6 - 10 = 30 - 10 = 20
x = 20
Therefore, the two numbers are 6 and 20 respectively.
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A girl is 6 years younger than her brother. The
product of their ages is 135. Find their ages.
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Work Shown:
x = brother's age, which is some positive whole number
x-6 = sister's age, since she is 6 years younger than her brother
The product is the result of multiplication, so we multiply x and (x-6) to get 135
x*(x-6) = 135
x^2-6x = 135
x^2-6x-135 = 0
Use the quadratic formula to solve from here
We plug in a = 1, b = -6, c = -135
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-6)\pm\sqrt{(-6)^2-4(1)(-135)}}{2(1)}\\\\x = \frac{6\pm\sqrt{576}}{2}\\\\x = \frac{6\pm24}{2}\\\\x = \frac{6+24}{2}\ \text{ or } \ x = \frac{6-24}{2}\\\\x = \frac{30}{2}\ \text{ or } \ x = \frac{-18}{2}\\\\x = 15\ \text{ or } \ x = -9\\\\[/tex]
x represents the brother's age, in years. So x must be positive.
Since x must be positive, this means we rule out x = -9
The value x = 15 is the only practical solution.
If x = 15, then x-6 = 15-6 = 9
The brother is 15 years old and the sister is 9 years old.
The product of their ages is 15*9 = 135, which confirms the answers.
I will give you brailnest answer
Answer:1/4 of is the correct answer d is the dependant variable.
Step-by-step explanation:
A box contains 20 red balls, 25 white balls, and 55 blue balls. Suppose that 10 balls are selected at random one at a time with replacement; that is, each selected ball is replaced in the box before the next selection is made. Determine the probability that at least one color will be missing from the 10 selected balls.
Answer:
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Determine the probability that at least one color will be missing from the 10 selected balls.
Red missing:
Each time, there are 55 + 25 = 80 non-red balls, out of 100. So, in each of the 10 trials, 80% = 0.8 probability of not picking a red ball. The probability that no red ball is picked is given by:
(0.8)^10 = 0.1074
White missing:
55 + 20 = 75 non-white balls, out of 100, in each trial. The probability that no white ball is picked is given by:
(0.75)^10 = 0.0563
Blue missing:
45 non-blue balls, out of 100. The probability that no blue ball is picked is given by:
(0.45)^10 = 0.0003
Total:
0.1074 + 0.0563 + 0.0003 = 0.164
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period. a. Which form of the null and alternative hypotheses most appropriate for this situation
The question is incomplete. The complete question is :
The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 24 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.
a. Which form of the null and alternative hypotheses most appropriate for this situation.
[tex]$H_0$[/tex]: is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24)
[tex]$H_a$[/tex]: is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24)
Solution :
It is given that the current mean sales volume in one month is 24 automobiles. The automobile dealership manager wants to conducts research study to check the increase in the sales volume due to the launch of a new bonus plan. So to collect the data on plan, sample of the sales personnel is allowed to sell for one month period only according to the new bonus plan.
Therefore the null hypothesis and the alternate hypothesis that most appropriates the situation is :
[tex]$H_0 \leq 24$[/tex][tex]$H_a > 24$[/tex]Find the area of the trapezoid
Answer:
1/2(l1+l2) is the area of trapezium
Answer:
A=a+b /2h
Step-by-step explanation:
The earth travels 1,050 miles per hour.
At this rate, how many miles does the earth travel per day?
Plz Help God will Bless You!!
The earth travels 1,050 miles in an hour.
There are 24 hours in a day.
So multiply 1,050 by 24.
And you get 25,200.
The earth travels 25,200 miles in a day.
Farmer brown uses super dip to ensure his cattles are free of parasites. What is the independent variable when cattles are devided into three groups?
Answer:
what are there any numbers
Step-by-step explanation:
Write the equation for
Twice a number added to five- and four-tenths is.
the same as the number minus two and nine-denths.
Answer:
Step-by-step explanation:
9/10 of a 70-foot-long driveway has already been paved. How many feet of the driveway has been paved?"
Answer:
63
Step-by-step explanation:
Please help me !!!!!!!!!
Answer:
f(-2) = 0
f(1) = 12
f(2) = 5
Step-by-step explanation:
f(-2) will lie in the function [tex] f(x) =x^2 - 4[/tex]
[tex]\therefore f( - 2) = {( - 2)}^{2} - 4 = 4 - 4 = 0 [/tex]
f(1) will lie in the function [tex] f(x) =2x^2 +10[/tex]
[tex]\therefore f(1) = 2 {(1)}^{2} + 10 = 2 + 10 = 12 [/tex]
f(2) will lie in the function [tex] f(x) =5[/tex]
[tex]\therefore f(2) = 5[/tex]
PLZZZ HELP IT'S FOR MIDDLE SCHOOLLLLL
jordans dog weighs p pounds emmett's dog weighs 25% more than jordan's dog which expressions represent the weight in of emmett's dog? a.0.25p b.1.25p c. p + 0.25 d. p + 1.25 e. p + 0.25p. Select two answers.
Answer:
B
Step-by-step explanation:
I think because if it weighs 25% more, then Jordans dog is the "1" part and Emmetts dog is the .25 part.
Answer:
B, 1.25p
Step-by-step explanation:
Lets say that Jordan's dog is a certain weight making him 1, It says Emmett's dog weighs 25% more, so that would give us 1.25. Now the reason is that it's B instead of C is that we have a p next to our 1.25. This means that its 1.25 x p, p being your pounds. So if you were to understand this equation, it would be, 1.25 x pounds. Let's also remember 1 x 1 = 1. So 1 x 1.25 is 1.25. 1 times anything is going to be the same number.
b. 3.3 x 0.8 =
3 3
х
8
Answer: the answer is 2.64 or 264
Explanation: if you multiply 3.3 × 0.8=264 but if you mulyiply 33×8=264
The data set shows the lengths, in minutes, of different musical performances.
36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20
What is the interquartile range (IQR) of the data set?
Answer: It has to be 22.5
Step-by-step explanation: Since this is a quiz, I won't tell you how to solve it, i'll give you some clues. But with what I know is; you have to find the (Q1) and (Q3) Then see what the difference is between the quartiles, and that should be your answer.
The interquartile range (IQR) of the data set is 19.
It is required to find the interquartile range (IQR) of the data set.
What is statistics ?Statistics are defined as numerical data, and is the field of math that deals with the collection, tabulation and interpretation of numerical data. It is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
Given:
The date are arranged from ascending order
9,14,15,18,20,22,29,36,36,42,45,51
Now you have one lower half with the numbers 9,14,15,18,20,22 and an upper half with the numbers 36,36,42,45,51.
As you can see in the figure, you have to find the median for these lower and upper halfs, so you have:
[tex]Q_{1} =16\\\\Q_{3} =35\\[/tex]
Now we can find the interquartile range that is:
[tex]IQR=Q_{3} -Q_{1}\\\\IQR=35-16\\\\IQR=19[/tex]
Therefore, the interquartile range (IQR) of the data set is 19.
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х 9 17 25 33 -6 -24 -96 -384 Is the relationship linear , exponential , or neither?
Answer:
exponential!!! That is the answer if this is for Khan Academy!!
math help #6 plzzzzz
Answer:
x = 30
m<2 = 94°
m<3 = 94°
Step-by-step explanation:
✔️m<2 = m<3 (vertical angles)
4x - 26 = 3x + 4 (substitution)
Collect like terms
4x - 3x = 26 + 4
x = 30
✔️m<2 = 4x - 26
Plug in the value of x
m<2 = 4(30) - 26
m<2 = 94°
✔️m<3 = 3x + 4
m<3 = 3(30) + 4
m<3 = 94
Oof please help me with geometry
Answer:
as it a cyclic quadrilateral
its opposite sides sum be 180
z/2+z/4+30=180
2z+z/4=150
3z/4=150...z=200
angles...
b=z/2=200/2=100
d=80
e=200-59=141
c=180-141=39
I can’t understand the graph
Autumn buys 5 hats at $8.99 each. How much does she spend?
Answer:
Autumn spends $44.95 On hats. Why would she need 5 hats? I don’t know.
Step-by-step explanation:
5 hats, all costing $8.99
You do 5*8.99, and this gives you $44.95
Answer:
5 x 8.99 = 44.95
Step-by-step explanation:
Please help, Dont guess :) will mark brainliest
Answer:
43 1/2Step-by-step explanation:
The formula to find the area of a triangle is multiplying base times height divided by 2.
So we have 3+3+3 (which is the base) times height. Finally we have: 9 x 11, which is 99 and now we divide it by 2. So 99/2 = 49 1/2.
Now we subtract the missing rectangle, which we can find by multiplying 3 by 2, which is 6.
So now subtract 6 from 49 1/2, and you'll get 43 1/2.
Answer:
43.5
Step-by-step explanation:
(( I will be using "*" as a multiplication sign ))
Area of rectangle = length * width = 3 * 2 = 6
Area of triangle = 1/2 bh = 1/2(11*9) = 1/2 of 99 = 99 divided by 2 = 49.5
So, since we are taking away the rectangle from the triangle, we will subtract the area of the rectangle from the triangle.
49.5 - 6 = 43.5
If you have any question please message me or comment
what is the value of h
Answer:
h = 5.318 m
Step-by-step explanation:
6.5/11 = h/9
0.5909 = h/9
h = 5.318
Answer:
Height: 5.32
Step-by-step explanation:
Area=29.24
Heron's Formula
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 houses. The subdivision was built in 1983. A sample of 120 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $229,500?
Answer:
0.0268 = 2.68% probability that the sample average is greater than $229,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single house:
The mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, which means that [tex]\mu = 228, \sigma = 8.5[/tex]
Sample:
Sample of 120, so, by the central limit theorem, [tex]n = 120, s = \frac{8.5}{\sqrt{120}} = 0.7759[/tex]
What is the probability that the sample average is greater than $229,500?
This is 1 subtracted by the pvalue of Z when X = 229.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{229.5 - 228}{0.7759}[/tex]
[tex]Z = 1.93[/tex]
[tex]Z = 1.93[/tex] has a pvalue of 0.9732
1 - 0.9732 = 0.0268
0.0268 = 2.68% probability that the sample average is greater than $229,500
Andre bought a new bag of cat food. The next day, he opened it to feed his cat. The graph shows how many ounces were left in the bag on the days after it was bought.
How much did the bag weigh before it was opened?
Answer:
There were 16 ounces of Cat Food after 24 days.
Find 30% of 70 whats your right one
Answer:
21
Step-by-step explanation:
I hope this helps!
1. Find the permeter of the triangle
(6x + 2) cm
(x- 4)cm
(3x + 1) cm
Lowest common multiple of 16 and 32?
Answer:
4
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
a book which cost 300 naira was sold for 240naira.what was the loss percentage?
Answer:
20%
Step-by-step explanation:
Since the original price of the book is 300 naira...
100% = 300 naira
1% = 300 ÷ 100 = 3 naira
240 ÷ 3 = 80
Since 80% is the percentage of the price after the loss..
100 - 80 = 20%
1. An airplane flies with a constant
speed of 740 miles per hour. How
far can it travel in 2 hours?
Answer:
740×2= 1480 in 2 hours
hope this helps :)
Describe or show two different ways to find the volume of a right rectangular prism with dimensions of 9 centimeters by 7 centimeters by 12 centimeters.
Answer:
9×7×12=756 is the dimensions
What is 3+3!!??!!??!!??!!??!!??!!??
Answer:
6
Step-by-step explanation:
cause 3+3 is 6
thanks for the easy points :3
Answer:
id.kkkkk.. maybe 5.. maybe 6...
:O
1. 3x = 18
2. 3 + x = 18
3. 17 - 6 = x
Help please
Answer:
1. 6
2. 15
3. 11
Step-by-step explanation:
