The expression -5g + 15h - 25 can be simplified as -5(g + 3h - 5)
ExpressionExpressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
In the question given, the expression is -5g + 15h - 25;
We have to simplify this to by factoring the expression.
-5g + 15h - 25 = -5(g + 3h - 5)
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In MNO, O≈ N, MN = 20 and NO = 14. Find OM.
The length of OM is 20 if MN=20 and N0=14
What is meant by an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.
To find the length of OM
Given,
MN=20
ON=14
∠O≅∠N
Since, ∠O≅∠N
ΔMNO is isosceles triangle with
OM=MN=20
Hence, the length of OM is 20.
Therefore, The length of OM is 20 if MN=20 and N0=14
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A kindergarten teacher has five books to distribute to 20 children in her class. (a) how many ways are there for her to distribute the books if they are all the same and no child gets more than one? (b) how many ways are there for her to distribute the books if they are different and no child gets more than one?
The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.
(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.
(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.
(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.
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The complete question is:
A kindergarten teacher has five books to distribute to 20 children in her class.
(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?
(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.
(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?
During a family vacation, the ratio of sunny days to rainy days was 12 to 5. What was the ratio of rainy days to the total number of days?
Answer: 5:17
Step-by-step explanation: Add both ratios together to get the complete amount of days.
Answer:
5:17
the rainy days amount is 5 and the total amount of days is 17 (12+5) so 5:17
consider a trial in which a jury must decide between the hypothesis that the defendant is guilty and the hypothesis that the defendant is innocent. in the framework of hypothesis testing and the u.s. legal system, which of the hypotheses should be the null hypothesis?
The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury.
Given that,
Think about a case where a jury must choose between the hypotheses that the defendant is guilty and the defendant is innocent.
We have to find which of the hypotheses ought to be the null hypothesis in the context of hypothesis testing and the American legal system.
We know that,
A jury in a trial must choose between two hypotheses. The null hypothesis is
H₀:The defendant is innocent
The alternative hypothesis or research hypothesis is
H₁ : The defendant is guilty
Which of the two hypotheses is correct is unknown to the jury. They must decide based on the information provided.
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a disease has hit a city. the percentage of the population infected t days after the disease arrives is approximated by p(t) for 0t. after how many days is the percentage of infected people a maximum? what is the maximum percent of the population infected?
The number of days would be 10 and the maximum percent of the population infected would be 25.752%.
What are exponential functions?
The exponential function, denoted by [tex]e^x[/tex], is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
[tex]p(t) = 7te^{-\frac{t}{10}}[/tex]
percentage of infected people a maximum when p '(t) = 0
[tex]p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10[/tex]
Hence percentage of infected people reaches a maximum after 10 days
maximum percent of the population infected = p(10)
[tex]p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%[/tex]
Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.
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Todd's living room is rectangular and measures 9 meters by 3 meters. Beginning in one corner, Todd walks the length of his living room and then turns and walks the width. Finally, Todd walks back to the corner he started in. How far has he walked? If necessary, round to the nearest tenth.
. There are 976 people working in an office. On a particular day, 61
people were absent. What percentage of the workforce did not show
up for work that day?
Answer: 6.25%
Step-by-step explanation:
To find what percent 61 is of 976, we divide 61/976. This comes out to be 0.0625. Multiply by 100 to get your percentage, and it's 6.25%.
You have 1 2/5 minutes left of
passing time. How many vines
can you watch if each vine is 6
seconds? (Hint: 6 seconds=
1/10 of a minute.)
Answer: You can watch 14 vines.
Step-by-step explanation: 1 2/5 is equal to 1 4/10
1 4/10 is equal to 14/10
So the amount of vines you could watch is 14 in 1 minute and 24 seconds.
How many solutions does the system of linear equations represented in the graph have?
Coordinate plane with one line that passes through the points negative 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 5 and 1 comma 3.
No solution
Infinitely many solutions
One solution at (−1, 3)
One solution at (3, −1)
The linear equations has one solution which is and the solution at (3, −1)
How to find the equations of the lineThe slope of the points (-3, -3) and (0, -2) is solved to get
m = (-2 - -3) / ( 0 - -3)
m = 1 /3
using point slope formula
y - -2 = 1/3(x - 0)
y + 2 = x/3
y = x/3 - 2
The slope of the points (0, 5) and (1, 3) is solved to get
m = (3 - 5) / (1 - 0)
m = -2
using point slope formula
y - 5 = -2(x - 0)
y - 5 = -2x
y = -2x + 5
solving simultaneously
y = -2x + 5
y = x/3 - 2
subtraction gives
0 = -7x/3 + 7
7x/3 = 7
x = 3 and y = -1
(3, -1) is the only solution
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What is 15% of a restaurant check for $65. 12? Explain how you calculated your answer. Round your answer to the nearest hundredth, if necessary.
Answer:
Step-by-step explanation:
if you do 65.12 * 15% you will get 9.768
subtract that from 65.12 you will get 55.352
round that to the nearest hundredth it is 55.35
find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) (-5,6)
The equation of the circle with endpoints of a diameter at the points (3, 8) and (-5, 6) is x² + y² + 2x - 14y + 33 = 0.
How to determine the equation of a circleThese are the specified parameters:
Endpoints of a diameter at the points (3, 8) and (-5, 6).
Determine the center point of the circle (a, b).
(a, b) = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
= ((3 + (-5))/2 , (8 + 6)/2)
= (-2/2 , 14/2)
= (-1, 7)
The center point is (-1, 7).
Determine the radius of the circle (r).
[tex]\begin{aligned} r & = \frac{1}{2} \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\r & = \frac{1}{2} \sqrt{(-5-3)^2 + (6-8)^2} \\ r& = \frac{1}{2} \sqrt{(-8)^2 + (-2)^2} \\ r& = \frac{1}{2} \sqrt{64 + 4} \\ r & = \frac{1}{2} \sqrt{68} \end{aligned}[/tex]
Determine of the equation of the circle
(x - a)² + (y - b)² = r²
(x - (-1))² + (y - 7)² = (1/2 √68)²
x² + 2x + 1 + y² - 14y + 49 = 1/4 × 68
x² + y² + 2x - 14y + 50 = 17
x² + y² + 2x - 14y + 50 - 17 = 0
x² + y² + 2x - 14y + 33 = 0
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Please answer this is due today
A 5-pound carton of oatmeal costs $6.25. What is the unit price? $__________ per pound (just type the number in the answer, not the $)
Answer: $1.25.
Step-by-step explanation: The unit price of the oatmeal is calculated by dividing the total cost by the weight of the carton. In this case, the unit price is $6.25 / 5 pounds = $1.25 per pound. This means that for every pound of oatmeal, the cost is $1.25.
Answer:
dang he beat me to it
Step-by-step explanation:
6.25/5 is 1.25 per pound
Solve while using the Pythagorean theorem! Please help
Answer:
Step-by-step explanation:
a^2 +b^2 =c^2
8^2 +14^2=y^2
64+196 =y^2
260=y^2
(260)^1/2 =y
Simplified: 4^1/2 * 65^1/2= 2(65^1/2)
g given 2n letters, two of each of n types, how many arrangements are there with no pair of consecutive letters the same?
The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).
Explain arrangements are there with no pair of consecutive letters the same.Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!
According to given information:So such plans where the sets of indistinguishable letters are discernible. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe
∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)
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Can you guys help me with this thanksss!!
Answer:
Step-by-step explanation:
What are you supposed to do
Trey lost 7 1/12 pounds in
8 weeks. If his weight loss
remained constant each week.
how many pounds did he
lose each week?
Answer:
about 15/16
Step-by-step explanation:
we are given a bag of 35 different colored chips. there are 20 black chips and 15 white chips. you draw 11 chips at random, what is the probability of getting 5 black chips and 6 white chips1 ?
The probability of getting 5 black chips and 6 white chips is [tex]\frac{7}{22}[/tex].
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to data in the given question,
We have the given information:
Total number of different colored chips = 35
Number of black chips = 20
Number of white chips = 15
And you draw 11 chips at random.
Now, we will calculate the probability of getting 5 black chips and 6 white chips,
[tex]P(B) = \frac{5}{20} =\frac{1}{4} \\P(W) = \frac{6}{15} =\frac{2}{5} \\P( black and white ) = \frac{\frac{1}{4}*\frac{2}{5}}{\frac{11}{35} } \\=\frac{\frac{1}{2}*\frac{1}{5}}{\frac{11}{35} }\\=\frac{1}{10}*\frac{35}{11}=\frac{7}{22}[/tex]
Therefore, the probability of getting 5 black chips and 6 white chips is 7/22.
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please help me now, much appreciated! I'll give brainliest if you answer!
By evaluating the piecewise function we will see that the difference is:
f(1) - f(-7) = 3
How to find f(1) - f(-7)?Here we have a piecewise function defined on the image, and we want to find the difference:
f(1) - f(-7).
First, let's find these values.
f(1) means that we need to evaluate the function in x = 1.
Notice that the second piece can be used on the domain 4 < x ≤ 1, so we need to use that part.
f(1) = -(1)^2 - 3*1
f(1) =-1 - 3 = -4
To evaluate in x = -7 we need to use the first piece of the function:
f(-7) = |-7 + 5| - 9
f(-7) = |-2| - 9 = -7
Then the difference is:
f(1) - f(-7) = -4 - (-7) = -4 + 7 = 3
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What type of variable is required to construct a confidence interval for a population​ proportion?.
A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes. So the correct option is D.
In the given question we have to find what type of variable is required to construct a confidence interval for a population proportion.
As we know that;
Population proportion is the percentage of the entire population that possesses the given quality (which is qualitative in nature). The confidence interval for the population proportion must thus be constructed using a qualitative variable with two possible outcomes.
So, the correct option is identified from nature of different type of the variables. A variable which is required to construct a confidence interval for population proportion is qualitative variable with two possible outcomes.
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The right question is:
What type of variable is required to construct a confidence interval for a population proportion?
A. Quantitative
B. Qualitative with any number of possible outcomes
C. Continuous
D. Qualitative with 2 possible outcomes
E. Discrete
F. Qualitative with 3 or more possible outcomes
-0.8x - 2.14 = -6.2 all my points
Answer: 5.072
Step-by-step explanation: -0.8-2.14=-6.2
+2.14 | +2.14
-----------------------------------------------------------------------------------------------
-4.06/-0.8=5.072
Lola has a collection of 432 trading cards, and Joel has a collection of 505
trading cards.
At the end of each month, Lola buys a box of 40 trading cards and Joel
buys a box of 32 trading cards.
After how many months will Lola have more trading cards than Joel?
Answer: 10 months
Step-by-step explanation:
432 + 40x >505 + 32x
40x >32x + 73
8x > 73
8x/8 > 73/8
x > 73/8 = 9.125
Round 9.125 to 10
The number of months that will take Lola to have more trading cards is obtained as 8.
What is linear inequality?Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.
Unlike a linear equation it can have a range of values inside an interval.
The number of cards with Lola and Joel are 432 and 505 respectively.
Suppose the number of required month be x.
Then, the inequality expression can be written for the given case as,
432 + 40x > 505 + 32x
⇒ 40x - 32x > 505 - 432
⇒ 8x > 63
⇒ x > 63/8
The number of months should be an integer value.
And, the nearest integer value of the greater than 63/8 is 8.
Hence, the number of months required for the given case is 8.
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Which is the solution for the system of
linear equations graphed below?
A. (-4,3)
B. (0, 1)
C. (0, 3)
D. (-3, 4)
Answer:
D. (-3, 4)
Step-by-step explanation:
Hope it helps!
A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.33 degrees. The camera is 196.0 cm above the surface. How far from the camera is the rock?
The distance between the rock and the surface is 827.20 cm.
Given data,
There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.
How far is the rock from the camera?
From the given data,
tan c = AB/BC
tan 13.33° = 196/BC
BC = 196/tan 13.33°
BC = 827.20 cm
Hence, the distance between the rock and the surface is 827.20 cm.
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Is it okay if ya'll can help me on number 5,8,9, and 10
The answer to the following algebra is;
b² at b = 4 is 16
y /5 at y = 15 is 3
27/s at s = 9 is 3
q/3 + 4 at q = 3 is 5
How to solve algebraic expression?Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
Given the following:
b² at b = 4
substitute b = 4
= 4²
= 4 × 4
= 16
y /5 at y = 15
substitute y = 15
= 15/5
= 3
27/s at s = 9
substitute s = 9
= 27/9
= 3
q/3 + 4 at q = 3
substitute q = 3
= 3/3 + 4
= 1 + 4
= 5
In conclusion, the algebraic expression is solved by substituting the value of the variables.
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a 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 10 feet above the ground?
If the top slips down the wall at a rate of 2 ft/s, then 3.476 ft/s fast the foot will be moving away from the wall when the top is 10 feet above the ground.
In the given question, a 15 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 2 ft/s.
We have to find how fast will the foot be moving away from the wall when the top is 10 feet above the ground.
As given, 15ft ladder dy/dt= -2y=13ft
Let the length be x and height be y
So from the Pythagorean theorem
x^2+y^2=h^2
Now apply the above formula to get the value
x^2+y^2=15^2
Take the derivative with respect to time
2x * dx/dt+2y*dy/dt=0
dx/dt= -y/x *dy/dt
When y = 13
then x^2+13^2=15^2
x = 7.48
dx/dt= -13/748 * (- 2)
dx/dt= 3.476 ft/s
Hence, if the top slips down the wall at a rate of 2 ft/s, 3.476 ft/s fast will the foot be moving away from the wall when the top is 10 feet above the ground.
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A pharmacist asserts that more than 40% of prescribed medicines are derived from plants. They decide to test this assertion by computing the sample proportion for a random sample. The data results in a test statistic of z = 2.14 and a P- value of .0162. Test at a 5% significance level. a. State the hypotheses for their test. I b. Briefly describe what the P-value is. c. Using the test statistic, how was the P-value found? d. Based on the P-value what conclusion should the pharmacist make? In particular, do they have enough evidence in support of their claim?
We reject the null hypothesis and come to the conclusion that their argument is adequately supported.
Given that,
z = 2.14 and p value = 0.0162
a) Hypotheses are
H₀ : p≤ 0.40
H₀ : p > 0.40 (claim)
This is right tailed test.
b) p value = 0.0162
c) Test statistic Z =2.14
P(Z>2.14) = 1 - P(Z≤2.14)
= 1 - 0.98382
= 0.01618
P value ≈ 0.01618
d) P value is less than α = 5% = 0.05
So, we reject the null hypothesis and conclude that they have enough evidence in support of their claim
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increasing the difference between sample means will result in what outcome in an independent-measures t-test?
Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.
What is the t - test?
When the population standard deviation is unknown, the student's t-test in statistics is a method for testing assumptions about the mean of a small sample taken from a population with a normally distributed sample size.
The independent samples t-test examines whether the two distinct values are different from one another when comparing two means, one of which is calculated from one set of scores and the other of which is calculated from another set of scores.
A two-sample t-test should be used to compare two independent means. The variances for both samples must be equal according to the test's premise.
Welch's test for unequal variances should be used if they are not.
Increase the probability of rejecting the null hypothesis and the size of the effect measurements.
Hence, Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.
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a study showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. to investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup. (a) formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the superma
As described in probability Null hypothesis is 0.64
what is probability?
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.
Solution:
Null hypothesis H0 : p = 0.64
Alternate hypothesis Ha : p ≠ 0.64
therefore Null hypothesis is 0.64
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The increase in price of an article is 20% . If the new price is $150 , what was the original price?
$600 is the original price of the article if the price of an article is 20% and new price is $150
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The increase in price of an article is 20%
The new price is $150
We need to find the original price of the article.
Let 20% of x=150
20/100x=150
0.2x=150
Divide both side by 0.2
x=750
Now subtract 750 and 150 we get original price
750-150
600
Hence, $600 is the original price of the article if the price of an article is 20% and new price is $150
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Combine the like terms to create an equivalent expression.
7k + 3k + 11 =
Stuck? Review related articles/videos or use a hint.
Answer:
When you combine like terms, you look for the same variable or look for constants. In this case, the same variable if 'k'. Now you add the coefficients 7 and 3, which is 10. So the expression simplifies to 10k + 11.
Hope this helps!
Answer:
10k + 11
Step-by-step explanation:
Like terms are terms that have the same amount of the same variables.
In this case, note that two of the terms have the variable "k" attached:
7k & 3k, respectively.
In this case, the question asks you to combine like terms, or to simplify the given expression:
7k + 3k + 11
(7k + 3k) + 11
10k + 11
10k + 11 is your answer.
~
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