At x=0
\(\begin{gathered} f(x)=14 \\ c=14 \end{gathered}\)at x=1
\(\begin{gathered} f(x)=10.5 \\ a+b=10.5-14 \\ a+b=-3.5 \end{gathered}\)at x=2
\(\begin{gathered} f(x)=8 \\ 4a+2b=8-14 \\ 4a+2b=-6 \end{gathered}\)a=1/2
So correct option is (c).
(7i)(3i) help please
Answer:
-21i
Step-by-step explanation:
\(i^{2}\) = -1
7*3=21
21 x -1 = -21
Answer:
-21
Step-by-step explanation:
A map says that 4 centimeters represents 10 kilometers. What is the real distance that 18 centimeters represents?
Answer:
The real distance that 18 centimeters represent is 45 kilometers.
Step-by-step explanation:
In this case, you can use a rule of three to find the real distance that 18 centimeters represent given that 4 centimeters represent 10 kilometers:
4 cm → 10 km
18 cm → x
x=(18*10)/4
x=45 km
According to this, the answer is that the real distance that 18 centimeters represent is 45 kilometers.
I need help and someone to explain what the name of polynomial based on its degree and number of terms means.
The Solution:
We are to name each of the polynomials based on their number of terms and degrees.
Thus, all the answers are correct as ticked in the above pictures.
Small tug boats pull cruise ships up and down rivers to prevent them from grounding. Cruise ships anchor 22 km away from the river port. A tug boat can travel 20 km downstream in the same time it takes it to travel 10 km upstream. If the speed of the current is 5 km/h, calculate the time it takes for the tug boats to travel downstream from the river port to the cruise ship .
Answer:
1.1 hour or 1 hour and 6 minutes
Step-by-step explanation:
Time is given by the distance divided by the velocity. If the time it takes the tugboat to travel 20 km downstream in the same time it takes it to travel 10 km upstream, then:
\(t_1=t_2\\\frac{20}{v_b+v_c}=\frac{10}{v_b-v_c}\\v_c=5\ km/h\\20v_b-100=10v_b+50\\10v_b=150\\v_b=15\ km/h\)
The velocity of the boat is 15 km/h. When traveling downstream, the current will favor the boat, therefore, the time required for it to travel 22 km downstream is:
\(t=\frac{22}{v_b+v_c} \\\t=\frac{22}{15+5}\\ t=1.1\ hour\)
It will take the boat 1.1 hour or 1 hour and 6 minutes.
i am grading papers. I have 2 purple stickers, 3 green stickers, and 5 yellow stickers. What is the probability that i use two yellow stickers on graded papers?
Answer:
2\10= 1\5
Step-by-step explanation:
you add all the stickers which equals 10. and what to figure out the probability of using 2 yellows so you put 2 over 10 and when you round it off you get 1\5
suppose you have the following data: x 1 2 3 4 5 6 y 24 29 28 42 33 41 and the lsrl is ŷ =. find the residual value for x = 1.
The residual value for x = 1 is 0. To find the residual value for x = 1, we need to plug in x = 1 into the equation for the least squares regression line (lsrl) that we have been given. The equation for the lsrl is ŷ = 5.5x + 18.5.
So, when x = 1, we have:
ŷ = 5.5(1) + 18.5
ŷ = 24
This means that the predicted value of y for x = 1 is 24.
To find the residual value, we need to subtract the predicted value of y from the actual value of y for x = 1.
The actual value of y for x = 1 is 24 (according to the data given).
So, the residual value for x = 1 is:
residual = actual value of y - predicted value of y
residual = 24 - 24
residual = 0
Therefore, the residual value for x = 1 is 0.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue.
==========================================================
Explanation:
We have the following:
There are 2 purple sections labeled "1" and "8". The probability of getting purple is 2/8.There are 2 yellow sections labeled "2" and "3". The probability of getting yellow is 2/8.There are 3 blue sections labeled "4", "5", and "6". The probability of getting blue is 3/8.There's only one orange section (labeled "7"). The probability of getting orange is 1/8.In short,
Probability of purple = 2/8Probability of yellow = 2/8Probability of blue = 3/8Probability of orange = 1/8Normally the goal is to reduce the fractions, but in this case it's better to keep them as they are. This allows for easier comparisons of other fractions.
------------
Now to look through the answer choices to see which are true, and which are false.
A) This is false because the probability of orange is 1/8, while the probability of purple is 2/8. We're twice as likely to get purple compared to orange. Statement A is backwards and therefore false.B) This is true. The probabilities of yellow and blue are 2/8 and 3/8 respectively. Compare the numerators to see that 2 < 3, so 2/8 < 3/8. Choice B is the final answer.C) This is false. We found that the probability of orange was 1/8, while the probability of yellow was 2/8. It's clear that 1/8 and 2/8 aren't equal. Or you could say \(1 \ne 2 \rightarrow 1/8 \ne 2/8\)D) This is false. The probabilities of purple and blue are 2/8 and 3/8 respectively. Like with choice C, it's clear that 2/8 and 3/8 aren't equal.solve 3(5y+2)–y=2(y–3)
Answer:
y= -1
Step-by-step Explanation:
3(5y +2)-y=2(y-3)
Distribute- 15y +6-y=2y -6
Combine variables- 15y-2y-y=-6-6
Add everything together- 12y= -12
Divide- y= -1
Answer:
y = -1
Step-by-step explanation:
Step 1. Expand the brackets.
3(5y + 2) - y = 2(y - 3)
(3 x 5y) + (3 x 2) - y = (2 x y) - (2 x 3)
15y + 6 - y = 2y - 6
Step 2. Simplify the expanded brackets (not always necessary but is in this case).
15y + 6 - y = 15y - y + 6 = 14y + 6
So
14y + 6 = 2y - 6
Step 3. Solve the equation.
14y + 6 = 2y - 6
+ 6 to both sides
14y + 12 = 2y
- 14y from both sides
12 = -12y
÷ 12 on both sides
1 = -y
flip the negative
-1 = y
Step 3. Write your answer.
y = -1
if line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?
Answer:
what do the lines look like
Step-by-step explanation:
a girl is having dinner with her friends, to enter the restaurant it's 20 and reservation is 15 per person p=people
Answer:
Step-by-step explanation:
20+(15×y)
Pets Survey
Pets No Pets Total
6th grade
28 23
7th grade 20 29
8th grade 12
Total 60
How many 7th graders were surveyed?
22
74
51
49
34
134
a yeast culture is growing at the rate of W'(t) = 0.3e^0.1t grams per hour. if the starting culture weighs 3 grams, what will be the weight of the culture, w(t), after t hours? after 7 hours?
To find the weight of the culture, we need to integrate the growth rate function W'(t) with respect to time t to get the weight function W(t):
W(t) = ∫ W'(t) dt + C
where C is the constant of integration. Since we know that the starting culture weighs 3 grams, we can use this initial condition to solve for C:
W(0) = 3 grams
∫ W'(t) dt + C = 3
∫ 0.3e^0.1t dt + C = 3
(3 e^0.1t / 0.1) + C = 3
30 e^0 + C = 3
C = 3 - 30
C = -27
Therefore, the weight function is:
W(t) = (3 e^0.1t / 0.1) - 27
To find the weight of the culture after 7 hours, we simply plug t=7 into the weight function:
W(7) = (3 e^0.1(7) / 0.1) - 27
W(7) = (3 e^0.7) - 27
W(7) ≈ 7.94 grams
Therefore, the weight of the culture after 7 hours is approximately 7.94 grams.
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4y 8x - 16 as a function
Answer:
The function form is:
f(x) = 2x - 8
A home improvement store is analyzing the pricing of a line of lawnmowers. These are the cost and revenue
functions for a month of business, where x represents the selling price of a lawnmower:
R(X) = -2.075x2 + 768x
C(x) = -134.625x + 8,4037.5
Which selling prices result in a profit that is greater than or equal to zero?
Select all the correct answers.
120
135
285
300
335
Answer:
135
285
300
Step-by-step explanation:
You buy a used car for $10,000. The value of the car decreases by22% each year. Approximately how much is the car worth in 3 years?
Answer:
The value will be $3,400 after 3 years
Step-by-step explanation:
Convert the percentage into the cash decrease each year, multiply that by 3 and then subtract $10,000 by the sum.
.22 x 10,000 = 2,200
2,200 x 3 = 6,600
10,000 - 6,600 = 3,400
algebra 1 9-12.hss-id.b.6 represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
In Algebra, when representing data on two quantitative variables, you can create a scatter plot to visually display the relationship between these variables. The scatter plot consists of points that represent individual data points, with one variable on the x-axis and the other on the y-axis.
In algebra, one important skill is being able to represent data on a scatter plot. This involves plotting two quantitative variables and visually analyzing how they are related.
The variables can be any numerical data points such as height and weight, age and income, or any other pair of quantitative measurements.
By analyzing the scatter plot, we can determine whether the variables have a positive or negative correlation, or whether they are independent of each other.
Understanding how to represent data on a scatter plot and analyzing the relationship between variables is an essential skill in algebra and in many other fields that use data analysis.
By examining the scatter plot, you can determine if there's a positive, negative, or no correlation between the variables, as well as identify any outliers or trends in the data.
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in the exponential equation y=2(3)x, what is the value of x when y=18
Answer: X= 2
Step-by-step explanation:
if you substitute the options witht the x in the equation. 2 is the only one that has 18 as the result.
Suppose that Z, is generated according to Z, = a₁ + ca; −1 + · ... +ca₁, for t≥ 1, where c is a constant. (a) Find the mean and covariance for Z₁. Is it stationary? (b) Find the mean and covariance for (1 − B)Z,. Is it stationary?
In this problem, we are given a sequence Z that is generated based on a recursive formula. We need to determine the mean and covariance for Z₁ and (1 - B)Z, and determine whether they are stationary.
(a) To find the mean and covariance for Z₁, we need to compute the expected value and variance. The mean of Z₁ can be found by substituting t = 1 into the given formula, which gives us the mean of a₁. The covariance can be calculated by substituting t = 1 and t = 2 into the formula and subtracting the product of their means. To determine stationarity, we need to check if the mean and covariance of Z₁ are constant for all time t.
(b) For (1 - B)Z,, we need to apply the differencing operator (1 - B) to Z,. The mean can be found by subtracting the mean of Z, from the mean of (1 - B)Z,. The covariance can be calculated similarly by subtracting the product of the means from the covariance of Z,. To determine stationarity, we need to check if the mean and covariance of (1 - B)Z, are constant for all time t.
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Jane has $30 and is saving at the rate of 57 per week. Susan has $50 and is saving at the rate of $3 per week.
When will they have the same amount of money?
The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $2.70. Today they made $244.60 from the 146 wraps sold. How many of the wraps sold were vegetarian?
Answer:
88 Vegetarian Wraps Sold.
Step-by-step explanation:
This is a System of Equations Problem.
Your Two Systems Are:
v(1)+c(2.7)=244.6 and c+v=146
c = chicken wraps and v = vegetarian wraps
Each chicken wrap costs $2.70 (2.7). Put the variable of c next to (2.7) meaning to multiply.
Each vegetarian wrap costs $1 (1). Put the variable of v next to (1)
244.60 (244.6) is the total amount of money made from selling the wraps. This will be the total of the equation.
v(1)+c(2.7)=244.6
Solve 2.7c+v=244.6 for v.
Add -2.7c to both sides.
2.7c+v+−2.7c=244.6+−2.7c
v=−2.7c+244.6
Substitute −2.7c+244.6 for v in c+v=146.
c+v=146
c+−2.7c+244.6=146
Simplify both sides of the equation.
−1.7c+244.6=146
Add -244.6 to both sides.
−1.7c+244.6+−244.6=146+−244.6
−1.7c=−98.6
Divide both sides by -1.7.
\(\frac{-1.7c}{-1.7} =\frac{-98.6}{-1.7}\)
c=58
Substitute 58 for c in v=−2.7c+244.6.
v=−2.7c+244.6
v=(−2.7)(58)+244.6
Simplify both sides of the equation.
v=88
Answer:
c=58 and v=88
88 vegetarian wraps were sold.
The function f(x) = -4.9x² + 17x + 0.6 describes the height in meters of a basketball x seconds after it has been thrown vertically into the air. Solve the following problem. If your answer is correct you will see an image appear on your screen. WHEN will the basketball reach its maximum height? Round your answer to 3 decimal places if necessary. Use your graph from screen 5 to help. Do not include units.
The basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
Define the term function?A function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented as an equation, a graph, a table of values, or a verbal description. For example, the function f(x) = 2x + 1 represents a relationship between the input x and the output 2x + 1.
To find the maximum height of the basketball, we need to find the vertex of the parabola represented by the function f(x). The vertex of x-coordinate is:
x = -b/2a
The coefficients of the quadratic equation a\(x^2\) + b\(x\) + c are a, b, and c. In this case, a = -4.9 and b = 17, so:
x = -17/(2*(-4.9)) = 1.735 (rounded to 3 decimal places)
Therefore, the basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
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What additional information is needed to prove the triangles are congruent by side-angle-side?
The corresponding angles and sides of the two triangles need to be given in order to prove congruence by side-angle-side.
In order to prove congruence by side-angle-side, the corresponding angles and sides of the two triangles must be given. The sides must be proportional, which means that two sides of one triangle must be equal to two sides of the other triangle, and the angles between these two sides must also be equal. In other words, if two sides of one triangle are equal to two sides of the other triangle, and the angle between those two sides is also equal, then the two triangles are congruent. This can be expressed as “If two sides and the included angle of one triangle are equal to the corresponding sides and angle of a second triangle, then the two triangles are congruent.” In order to prove congruence by side-angle-side, all of the corresponding sides and angles must be given in order to show that they are equal.
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The additional information that is needed to prove the triangles are congruent by Side-Angle -Side us that the corresponding angles and sides of the two triangles need to be given .
What is Side-Angle-Side Congruence ?
The Two Triangles can be called as Congruent by Side-Angle-Side rule if any 2 sides and angle included between sides of one triangle is equivalent to corresponding 2 sides and angle between sides of second triangle .
In order to prove the Congruence by Side-Angle-Side, the corresponding angles and the sides of the 2 triangles must be given.
The sides must also be in proportional, that means that the two sides of one triangle must be equal to two sides of other triangle, and
the angles between these two sides of the triangle must be equal.
So , In order to prove a triangle congruent by Side-Angle-Side, all of the corresponding sides and angles must be given in order to prove that they are equal.
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in the united states, according to a 2018 review of national center for health statistics information, the average age of a mother when her first child is born in the u.s. is 26 years old. a curious student at cbc has a hypothesis that among mothers at community colleges, their average age when their first child was born is lower than the national average. to test her hypothesis, she plans to collect a random sample of cbc students who are mothers and use their average age at first childbirth to determine if the cbc average is less than the national average. use the dropdown menus to setup this study as a formal hypothesis test. [ select ] 26 [ select ] 26
To set up this study as a formal hypothesis test, the null hypothesis (H0) would be that the average age of first childbirth among mothers at community colleges (CBC) is equal to the national average of 26 years old.
The alternative hypothesis (Ha) would be that the average age of first childbirth among CBC mothers is lower than the national average.
The next step would be to collect a random sample of CBC students who are mothers and determine their average age at first childbirth. This sample would be used to calculate the sample mean.
Once the sample mean is obtained, it can be compared to the national average of 26 years old. If the sample mean is significantly lower than 26, it would provide evidence to reject the null hypothesis in favor of the alternative hypothesis, supporting the student's hypothesis that the average age of first childbirth among CBC mothers is lower than the national average.
The student plans to conduct a hypothesis test to determine if the average age of first childbirth among mothers at CBC is lower than the national average.
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Which rules is used to find the number of positive integers less than 1000 that are divisible by 7 but not by 11?
There are 130 positive integers less than 1000 that are divisible by 7 but not by 11.
The rule used to find the number of positive integers less than 1000 that are divisible by 7 but not by 11 is the inclusion-exclusion principle. This principle states that if we want to find the number of elements that belong to at least one of two sets, we can add the sizes of the sets together and then subtract the size of the intersection of the sets. In this case, we first find the number of positive integers less than 1000 that are divisible by 7 (which is 142), then the number that are divisible by 11 (which is 90), and finally the number that are divisible by both (which is 12). Using the inclusion-exclusion principle, we can find the number of positive integers less than 1000 that are divisible by 7 but not by 11 by subtracting the number that are divisible by both from the number that are divisible by 7: 142 - 12 = 130. Therefore, there are 130 positive integers less than 1000 that are divisible by 7 but not by 11.
To find the number of positive integers less than 1000 that are divisible by 7 but not by 11, you can use the Inclusion-Exclusion Principle.
First, find the number of integers divisible by 7: there are 999/7 = 142.71, so 142 integers are divisible by 7.
Next, find the number of integers divisible by both 7 and 11 (i.e., divisible by their LCM, which is 77): there are 999/77 = 12.97, so 12 integers are divisible by 77.
Now, apply the Inclusion-Exclusion Principle: Subtract the number of integers divisible by both 7 and 11 from the number of integers divisible by 7: 142 - 12 = 130.
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What is f(5) for the function f(x) = 7x +4?
f(5)=
Answer:
f(5) = 39
Step-by-step explanation:
can somebody help me with this question?
Answer:
x = 10
z = 97
Step-by-step explanation:
Mike's truck engine holds 1 and 1/4 gallons of oil if there are 3 quarts of oil in the engine now how many more quarts of oil does Mike need to fill the engine to capacity
Answer:
2 more quarts of oil is needed to fill
the engine to capacity
Step-by-step explanation:
Here, we want to calculate how many more quarts of oil is required to fill the engine to capacity
We have to convert the capacity to quarts
Mathematically, 1 gallon = 4 quarts
So 1 1/4 gallon will be 5/4 * 4 = 5 quarts
So the number of quarts needed to fill the engine to capacity will be 5 quarts - 3 quarts = 2 quarts
The odds of an event happening is 5/9. What are the odds in favor of the event happening ?
When a number is increased by 9.5%, the result is 58. What is the original number to the nearest tenth?
(I've seen other questions like this, but the answer is wrong. It's not 50 or 52.49 or 52.5.)
Answer:
53
Step-by-step explanation:
58÷1.095= 53 is the answer
Answer:
5.03196347032
Step-by-step explanation:
We do:
.095x+x=58
1.095x=58
x=52.96
52.96 is a approximation and when you do the math and see what 9.5 of 52.96 plus 52.96 is you get 57.9912 which is super close to 8 The exact answer is x = 5.03196347032
In general, higher confidence levels provide: a)narrower confidence intervals b)a smaller standard error c)wider confidence intervals d)unbiased estimates
In general, higher confidence levels provide wider confidence intervals.
What is the concept of confidence level and confidence interval?
Confidence level:
The confidence level refers to the long term success rate of the method , that is , how often this type of interval will capture the parameter of interest.
Confidence interval:
A specific confidence interval gives a range of plausible values for the parameter of interest.
As the confidence level increases, the width of confidence interval also increases.
A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means the interval is larger.
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