Answer:
[tex]\frac{g}{8}-17[/tex] games
Step-by-step explanation:
Employees: 8
Sales last month: g
Average: [tex]\frac{totalGames}{Employees}[/tex]
To find out how many games Chris sold, we have to take the average and subtract 17.
[tex]\frac{g}{8}-17[/tex]
Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.
Answer:
g over 8 -17
Step-by-step explanation:
A bag contains 1 blue, 2 green, and 3 red marbles, as shown. What is the probability of drawing a green marble out of the bag without looking?
ANSWER
[tex] P(G)= \frac{1}{3}[/tex]
EXPLANATION
The number of green marbles in the bag is
[tex]n(G) = 2[/tex]
The total number of marbles in the bag is
[tex]n(S)=1+2+3 = 6[/tex]
The probability of selecting a green marble from the bag without looking is
[tex]P(G)= \frac{n(G)}{n(S)} [/tex]
Substitute the values to get,
[tex]P(G)= \frac{2}{6} [/tex]
[tex]P(G)= \frac{1}{3} [/tex]
Answer:
The probability of drawing a green marble out of the bag without looking = 1/3
Step-by-step explanation:
It is given that, a bag contains 1 blue, 2 green, and 3 red marbles
Therefore total number of marble in the bag = 1 + 2 + 3 = 6
To find the probability
Total number of marble = 6
Number of green marble = 2
The probability of drawing a green marble = 2/6 = 1/3
It was 8 degrees at nightfall. The temperature dropped 10 degrees by midnight. what was the temperature at midnight?
Answer: The temperature would be -2 degrees at midnight.
Step-by-step explanation:
If you take 8 and minus 10 then you get -2!
Answer:
-2
Step-by-step explanation:
hope it will help youu!!!
A gear in a watch turns clockwise, in 1° sections, a total of 300 times. How many degrees has the gear turned?
Answer:
300°
Step-by-step explanation:
This may seem really strange and counterintuitive to you, but when you turn 1° 300 times, you have turned 300°.
_____
If you don't want to add it up ...
1° + 1° + 1° ... + 1° . . . . . 300 times
you can use multiplication. It was invented as a shortcut to repeated addition:
1° × 300 = 300°
The gear has turned a total of 300 degrees.
To solve this problem, we need to consider the information given and apply basic multiplication. The gear turns in 1° sections, and it does so a total of 300 times. Since each section is 1°, we can simply multiply the number of sections by the size of each section to find the total degrees turned.
So, the calculation is as follows:
Number of sections = 300
Size of each section = 1°
Total degrees turned = Number of sections × Size of each section
Total degrees turned = 300 × 1°
Total degrees turned = 300°
Therefore, the gear has turned 300 degrees in total.
For questions 4-5, how many solutions does the system have?
4. -4y+4=x
2x+8y=8
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
5. 6x+2=y
3y-18x=12
A. One Solution
B. Two Solutions
C. Infinitely Many Solutions
D. No Solution
Answer:
[tex]\large\boxed{Q4.\ C.\ \text{Infinitely Many Solutions}}\\\boxed{Q5.\ D.\ \text{No Solution}}[/tex]
Step-by-step explanation:
[tex]Q4.\\\\\left\{\begin{array}{ccc}-4y+4=x&(1)\\2x+8y=8&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(-4y+4)+8y=8\qquad\text{divide both sides by 2}\\-4y+4+4y=4\qquad\text{combine like terms}\\4=4\qquad\bold{TRUE}\\\\\text{Infinitely Many Solutions}[/tex]
[tex]Q5.\\\\\left\{\begin{array}{ccc}6x+2=y&(1)\\3y-18x=12&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3(6x+2)-18x=12\qquad\text{divide both sides by 3}\\6x+2-6x=4\qquad\text{combine like terms}\\2=4\qquad\bold{FALSE}\\\\\text{No Solution}[/tex]
Is there a way to calculate sin, cos, and tan without a calculator?
If so, could you please do it with this problem...
Tan(90°) = DE/4
Also, could you please explain it step by step.
Thanks!
Answer:
yes, and no
Step-by-step explanation:
There are a few trig functions that are "simple" and can be memorized. Usually, these are the ones for angles of 0°, 30°, 45°, 60°, 90°. See below for a table.
To solve an equation like this for DE, you multiply both sides of the equation by 4 (cancelling the denominator).
4·tan(90°) = DE
The tangent of 90° is "infinity." So, the length of DE will be infinite for an angle of 90°.
_____
Trig functions of multiple angles and half angles can be derived from those in the table using the appropriate formulas. The math can get messy fast.
Of course, SOH CAH TOA reminds you of the relationships between trig function values and right triangle side measures. You may not know the angle measure (and it may be irrelevant), but you can find the trig function value.
Answer:
See below.
Step-by-step explanation:
You can find them by constructing a right angled triangle with the given angle and measuring the sides giving sin = opposite / hypotenuse , cos = adjacent / hypotenuse and tan = opposite / adjacent ( SOH-CAH-TOA).
For tan 90 degrees you think of an 'imaginary' triangle where opposite side = hypotenuse and the adjacent side = 0 ( in fact a vertical line!) .Now tan x = opposite / adjacent = opposite / 0 which is indeterminate. There is no value for the tan of 90 degrees and so there is no solution to your problem.
A rectangular prism has the dimensions 8 feet by 3 feet by 5 feet. What is the surface area of the prism?
Answer:
A=158
Step-by-step explanation: SA = 2 × l × w + 2 × l × h + 2 × w × h
Answer: Option D
(D) 158 square feet
Step-by-step explanation:
A=2(wl+hl+hw)=2·(3·8+5·8+5·3)=158ft²
Graph the function. Describe its position relative to the graph of the indicated function
Answer:
C
Step-by-step explanation:
If the parent function is function [tex]y=f(x)[/tex] and [tex]a>0,[/tex] then
the graph of the function [tex]y=f(x-a)[/tex] is translated a units to the right graph of the parent function; the graph of the function [tex]y=f(x+a)[/tex] is translated a units to the left graph of the parent function;the graph of the function [tex]y=f(x)+a[/tex] is translated a units up graph of the parent function;the graph of the function [tex]y=f(x)-a[/tex] is translated a units down graph of the parent function.In your case, the grapgh of the function [tex]y=2^x+2[/tex] is translated 2 units up the graph of the function [tex]y=2^x.[/tex]
Answer:
To graph the function, we first need to know what means:[tex]f(x)=2^{x} +2[/tex] relative to [tex]f(x)=2^{x}[/tex]
This is called translation of functions, and it refers to the movement of a specific function, either upwards, downwards, leftwards or rightwards. To be able to translate a function, we have to use the next rules.
Moving upwards or downwards.If we sum a number to the whole function, we are gonna move that function upwards. For example, if we have [tex]f(x)=x^{2}[/tex] and sum 3 to it, we would have [tex]f(x)=x^{2} +3[/tex], which is the same function but moved 3 units upwards.If we subtract a number to the whole function, we are gonna move that function downwards. For example, if we have [tex]f(x)=x^{2}[/tex] and subtract 3 from it, we would have [tex]f(x)=x^{2} -3[/tex], which is the same function but moved 3 units downwards.In this case, the problem is saying that we have to move the function upwards by two units, because [tex]f(x)=2^{x} +2[/tex] is the same function as [tex]f(x)=2^{x}[/tex], but moved 2 units upwards.
In addition, the graph is attached, there you can see the difference between those two functions, you will se that they are the same, but one is moved two units upwards.
Given the table below for selected values of f(x), use 6 left rectangles to estimate the value of
.
x
1
3
4
6
7
9
10
f(x)
4
8
6
10
10
12
16
Numerical Answers Expected!
Answer for Blank 1:
Divide the area into 6 portions and find the sum of each one to find the value of the final integral:
f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2
= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units
Answer:
Step-by-step explanation:
Given is a table of x, f(x) as below
x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16
Mid pt 6 7 8 10 11 14
width of
interval 2 1 2 1 2 1
dA1 12 7 16 10 22 14
area = area of all rectangles= 81 sq units.
lily worked 3 hours more than andrea. together they worked a total of 16 hours. andrea worked a hours. Which equation represents this situation?
A. a+3=16
B. a+6=16
C. a+(a-3)=16
D. a+(a+3)=16
Answer:
The times were Lily 9.5 hours and Andrea 6.5 hours.
Equation "D" is correct using those numbers.
Step-by-step explanation:
Jill measured the length of her eraser. She wrote 5 on her paper without the unit which metric unit of measure should Jill include?
Answer:
Centimeter
Step-by-step explanation:
Erasers are pretty small so I would say it was about 5 cm.
Can anyone please help me!? Help!
Subject: Expanding and Simplifying Expressions
7th-grade Mathematics!
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Question #1: Write an expression that is equivalent to 2/3 (4x + 9).
A) 8/3x + 6
B) 8/3x + 9
C) 2/3x + 6
D) 2/3x + 9
-------------------------------------------------------------------------------------
Question #2: Which expression is equivalent to 1/3p + 15?
A) 1/3(p + 45)
B) 1/3(p + 5)
C) 3(p + 45)
D) 3(p + 5)
Answer:
[tex]\large\boxed{Q\#1.\ A)\ \dfrac{8}{3}x+6}\\\boxed{Q\#2.\ A)\ \dfrac{1}{3}(p+45)}[/tex]
Step-by-step explanation:
[tex]Q\#1:\\\\\dfrac{2}{3}(4x+9)\qquad\text{use the distributive property}\\\\=\left(\dfrac{2}{3}\right)(4x)+\left(\dfrac{2}{3}\right)(9)=\dfrac{8}{3}x+(2)(3)=\dfrac{8}{3}x+6\\\\Q\#2:\\\\\dfrac{1}{3}p+15=\dfrac{1}{3}p+\dfrac{1}{3}\cdot(3)(15)=\dfrac{1}{3}p+\dfrac{1}{3}\cdot45=\dfrac{1}{3}(p+45)[/tex]
On a winter morning, the temperature before sunrise was 11 degrees. The temperature then rose by 1/2 degree each hour for 7 hours before dropping by 2 1/4 each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours/
Answer:
7.75 F
Step-by-step explanation:
you will do 7/2 *
convert 2.25 to imporper fraction
multiply the denomintor
Answer:
7.75
Step-by-step explanation:
What is the value of the square root of 15 to the nearest tenth? Show or explain how you got your answer.
Answer:
3.9
Step-by-step explanation:
A calculator is useful for this.
Courney buys 2bags of apples.Each bag has 20 apples.How many apples does she buy?
Find the measure of angle B.
A) 90
B) 180
C) 120
D) 60
Answer:
C) 120 degrees
Step-by-step explanation:
m<A + m<B + m<C = 180
45 + m<B + 15 = 180
m<B + 60 = 180
m<B = 120
The answer is C) 120
Marissa bought 2 1/2 of a gallon of orange juice to make punch how many qaurts of orange juice did marissa buy?
Answer:
10 quarts
Step-by-step explanation:
There are 4 quarts to a gallon, and she bought 2 1/2 gallons, or 2.5 gallons, so she bought 4(2.5) = 10 quarts
Find the value of x and the value of y.
This would be D cause these are 30,60, 90 angles. 30 (X) 60(X square root of 3 and 90 2x).
Answer:
C
Step-by-step explanation:
Using the sine ratio on the right triangle on the right side
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{8}[/tex]
Multiply both sides by 8 × sin30° = y
⇒ y = 8 × [tex]\frac{1}{2}[/tex] = 4 → C
Susan collected 1,470 stickers and placed them in her sticker book if there are 35 stickers on each page of her sticker book how many pages of stickers does Susan have
All you need to do is divide 1470 by 35, which is 42.
What is the coefficient of q in the sum of these two expressions
(2/3q-3/4(-1/6q-r)
The coefficient of q in the sum of the two expressions is 17/24.
We have,
The given expression is:
(2/3q - 3/4(-1/6q - r))
Let's simplify this expression step by step:
Step 1: Distribute -3/4 to (-1/6q - r):
(2/3q - 3/4 * -1/6q + 3/4 * r)
Step 2: Simplify the multiplication of fractions:
(2/3q + 1/8q + 3/4 * r)
Step 3: Combine like terms:
(17/24q + 3/4 * r)
Thus,
The coefficient of q in the sum of the two expressions is 17/24.
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The coefficient of q in the sum of the expressions is found by simplifying the terms individually and then combining them. After finding a common denominator and adding the terms, the coefficient of q is 19/24.
Explanation:To find the coefficient of q in the sum of the given expressions (2/3q - 3/4*(-1/6q - r)), we first need to simplify the expression step by step. Starting with the second term, we distribute the -3/4 across the parentheses:
-3/4 * (-1/6q) = 3/4 * 1/6 * q = 1/8q-3/4 * (-r) = 3/4 * rNow adding this to the first term:
(2/3q + 1/8q) - (3/4)rTo add the q terms, they need to have a common denominator. The common denominator for 3 and 8 is 24. We convert both fractions:
2/3q = (2*8)/(3*8)q = 16/24q1/8q = (1*3)/(8*3)q = 3/24qNow we can add them:
16/24q + 3/24q = 19/24qThe coefficient of q in the sum of the given expressions is 19/24.
(2CQ) Write the repeating decimal as a fraction .15
Answer:
c. [tex]\frac{5}{33}[/tex]
Step-by-step explanation:
The given decimal is [tex]0.\bar {15}[/tex]
Let [tex]y=0.\bar {15}...(1)[/tex]
Multiply equation (1) by 100.
[tex]100y=15.\bar {15}...(2)[/tex]
Subtract equation (1) from equation (2)
[tex]\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}[/tex]
[tex]\Rightarrow 99y=15[/tex]
Divide both sides by 99.
[tex]\Rightarrow y=\frac{15}{99}[/tex]
Simplify;
[tex]\Rightarrow y=\frac{5}{33}[/tex]
The recurring decimal 0.15 can be converted to the fraction 5/33.
To convert the repeating decimal 0.15 to a fraction, follow these steps:
Let x be the repeating decimal: x = 0.151515...
Express this equation by multiplying both sides by 100 to shift the decimal point two places: 100x = 15.151515...
Next, subtract the original equation from this new equation: 100x - x = 15.151515... - 0.151515...
This simplifies to: 99x = 15
Solve for x by dividing both sides by 99: x = 15/99
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3: x = 5/33
Therefore, the repeating decimal 0.15 can be expressed as the fraction 5/33.
Which is an equation of a direct proportion? y=−2x y=12x−2 y=−2x+3 y=4x
Answer: First option and last option.
Step-by-step explanation:
By definition, an equation of direct proportion has the following form:
[tex]y=kx[/tex]
Where k is the constant of proportionality.
The equation of the line [tex]y=mx+b[/tex], where m is the slope and b the y-intercept.
When b=0, means that the line passes through the origin. Therefore, it would be:
[tex]y=mx[/tex]
(which is similar to [tex]y=kx[/tex])
Then, the slope of the line would be the constant of proportionality.
By definition, the slope can be positive or negative.
Keeping on mind the information above, you can see that the equation that have that form are:
[tex]y=-2x\\\\y=4x[/tex]
Answer:
y=−2x
Step-by-step explanation:
I got it right on Imagine math.
What is the discriminant of the polynomial below? 2x^2+3x-7
Answer:
Option C. [tex]65[/tex]
Step-by-step explanation:
we know that
The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]D=b^{2}-4ac[/tex]
in this problem we have
[tex]2x^{2} +3x-7[/tex]
so
[tex]a=2\\b=3\\c=-7[/tex]
substitute
[tex]D=3^{2}-4(2)*(-7)[/tex]
[tex]D=9+56[/tex]
[tex]D=65[/tex]
The discriminant of the giving polynomial is 65. The correct option is C. 65
The discriminant of a quadratic functionFrom the question, we are to determine the discriminant of the given polynomial
The given polynomial is
2x²+3x-7
This is a quadratic function
The discriminant of a quadratic function is simply the value in the square root of the quadratic formula
That is,
Discriminant, D = b² - 4ac
In the given quadratic function, 2x²+3x-7
a = 2, b = 3 and c = -7
∴ D = 3² -4(2)(-7)
D = 9 +56
D = 65
Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65
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Write the recursive formula and the explicit formula for the sequence {-15,-7,1,9, 17,...}.
ANSWER
Explicit formula:
[tex]a_n= 8n - 23[/tex]
Recursive
[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]
EXPLANATION
The first term of the sequence is
[tex]a_1=-15[/tex]
The common difference is
[tex]d = - 7 - - 15[/tex]
[tex]d = 8[/tex]
The nth term is given by the formula,
[tex]a_n=a_1 + d(n - 1)[/tex]
[tex]a_n= - 15+ 8(n - 1)[/tex]
[tex]a_n= - 15+ 8n -8[/tex]
The explicit formula is;
[tex]a_n= 8n - 23[/tex]
The recursive definition is
[tex]a_{n}= a_{n - 1} + 8,a_1=-15[/tex]
You get paid $18 for 3 hours of work. How much money would make if you worked 7 hours?
Answer:
$42
Step-by-step explanation:
Divide $18 by 3 to get a unit rate of $6 per hour. Then, multiply by 7 hours to get $42.
Grades on a standardized test are known to have a mean of 1000 for students in the US. The test is administered to 453 randomly selected students from Queens College, and they obtained an average grade of 1013 and a standard deviation of 108. a. Construct a 95 % confidence interval for the true average test score for Queens College students. b. With 5% significance level, Is there a statistical evidence that Queens College students perform differently than other students in the US? The same 453 students selected earlier are now given a two-hour tutoring session and then asked to take the test a second time. The average change in their test scores is 9 points, and the standard deviation of the change is 60 points. Assume the changes are from a Normal distribution. c. You are asked by the school administration to study whether students have performed better in their second attempt. State in terms of , the relevant null and alternative hypothesis in conducting this study. d. Compute the t statistic for testing against ; obtain the p- value for the test. e. Do you reject at the 5% level? At the 1% level? f. Provide a short summary of your conclusions from this study. Comment on the practical versus statistical significance of this estimate.
Answer:
a: 1003 < µ < 1023
b: See attached photo for answers
c: see below
d and e: See second attached photo
f: See below
Step-by-step explanation:
a. to find a confidence interval, first find the error with the formula,
E = Z(σ/√n) where Z is the value of the z-score that relates to the confidence level, σ is the standard deviation of the population (or of the sample if the population standard deviation isn't given), and n is the sample size
For this problem, E = 1.96(108/√453) = 9.95 = 10
Now add and subtract that value form the sample average...
x - E < µ < x + E becomes 1013 - 10 < µ 1013 + 10
simplifies to 1003 < µ < 1023
b. See attached photo for hypothesis test results...
c. H0: µ = 1013
Ha: µ > 1013 (claim)
They want to test if it's greater than their first attempt, so this claim becomes the alternate hypothesis. We're testing against their first attempt, that's why µ = 1013, not 1000
d and e. See second attached photo for hypothesis test results...
f. There is enough evidence to support the claim that the students second attempt was an improvement from their first attempt. They happened to take a 2 hour tutoring course between tests. This doesn't prove that the tutoring was effective thought. It very well might have been effective, but also, the students taking the test again means they've already seen the test and know what to expect, which could have also boosted their scores.
Explain how to solve 4x 2- 5x = 16 by completing the square. What are the solutions?
How would you solve mathematical problem?
Answer:
[tex]r=\dfrac{I}{Pt}[/tex]
Step-by-step explanation:
Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.
Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:
[tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]
What is the value of x in the equation 3(2x + 4) = ?6? (4 points) ?3 1 12 19
Answer:
2
Step-by-step explanation:
3(2x + 4)=?
6x + 12
6x/6=x
12/6=2
x=2
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 times.
Rolling a 5 in 300 rolls: Probability of 1/6 [tex]*[/tex] 300 ≈ 50 times.
Sure, let's break it down step by step:
1. Understand Experimental Probability : Experimental probability is based on actual outcomes from an experiment or trial. It's calculated by dividing the number of favorable outcomes by the total number of outcomes.
2. Identify the Probability of Rolling a 5 : Since a standard number cube has 6 faces numbered 1 through 6, each face has an equal probability of 1/6 of showing up in a single roll.
3. Calculate the Probability of Rolling a 5 : The probability of rolling a 5 is 1/6, since there's one favorable outcome (rolling a 5) out of the total 6 possible outcomes.
4. Use Probability to Predict Outcomes : To predict how many times you'll roll a 5 in 300 rolls, multiply the probability of rolling a 5 by the total number of rolls.
Let's calculate:
Probability of rolling a 5 = 1/6
Total number of rolls = 300
Number of times you'll roll a 5 = (Probability of rolling a 5) * (Total number of rolls)
= (1/6) [tex]*[/tex] 300
≈ 50
So, based on experimental probability, you can predict that you will roll a 5 approximately 50 times if you roll the number cube 300 times.
A poll reported that 66% of adults were satisfied with the job the major airlines were doing. suppose 15 adults are selected at random and the number who are satisfied is recorded. complete parts (a) through (e) below.
The statistical technique applicable here is simple random sampling and binomial distribution. The formula for a binomial distribution is used to estimate the probabilities of a specific number of satisfactions among the randomly selected 15 adults. The average number and variability can also be calculated for this binomial distribution.
Explanation:This question is about statistics, particularly a technique called simple random sampling. In the given scenario, it's reported that 66% of adults are satisfied with the major airlines' job. We're asked to conjecture about a scenario where 15 adults are chosen at random and the number who are satisfied is observed.
First, this scenario is modeled with a binomial distribution. A binomial distribution is appropriate here because you're considering a certain number of 'trials' (15 adults), and for each trial, there are two possible outcomes - the adult is either satisfied or not satisfied with the airlines. The 'success' probability (satisfaction) remains constant (66%).
A. If we want to know the probability of exactly x adults satisfied, the formula for a binomial distribution is used: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where C(n, k) is combinations of n things taken k at a time, n is number of trials (15), p is the probability of success (66% or 0.66), and k is the number of successes we want exact probability for.
B. If we want to know the expected value or the average number of adults satisfied, it's simply n*p, in this case 15*0.66 = 9.9, meaning, on average, about 10 adults out of 15 should be satisfied according to the poll report.
C. If we want to compute the variability, we can calculate the standard deviation. For a binomial distribution, the standard deviation, sigma, is square root of [ n*p*q ], where q = 1-p is the probability of 'failure', or an adult not satisfied.
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