The value of c after solving the equation is 8.
For the polynomial to be divisible by x+2, hence x = -2
Given
p(x) = 4x³+cx²+x+2
p(-2) = 4(-2)³+c(-2)²+(-2)+2
p(-2) = 4(-8) + c(4)-2+2
p(-2) = -32+4c
If p(-2) = 0
0= -32+4c
-4c = -32
c = 32/4
c = 8
Hence we get the value of c as 8.
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A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
5 salami sandwiches
16 salami sandwiches
30 salami sandwiches
24 salami sandwiches
A local deli makes turkey sandwiches and salami sandwiches at a weekly ratio of 2 salami sandwiches for every 5 turkey sandwiches. If the deli makes 60 turkey sandwiches this week, how many salami sandwiches did they make?
5 salami sandwiches
16 salami sandwiches
30 salami sandwiches
24 salami sandwiches
2 to 5 = x to 60
60/5 = 12
2 * 12 = 24
1.5(6t+2) i need help with problem let me know if one of yall ppl get the answer so i can finish my homework sheet pls and thank you!!!
The value of the expression illustrated as 1.5(6t+2) is 9t + 3.
What is the value of the expression?Expression is simply used in Mathematics to show the relationship between the variables that are illustrated. In this case, this depicts the information given.
Based on the information, the expression is illustrated as:
1.5(6t+2)
Open the parentheses
(1.5 × 6t) + (1.5 × 2)
= 9t + 3.
The value is 9t + 3.
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Complete question
Find the value of the expression given 1.5(6t+2) i
Let x and y be some integers. Consider the following statement: If xis odd and y is odd, then xy is odd. Proof. Assume that x is odd and y is odd. Then there exists some k integers such that x=2k+1 and m=2k+1. Then xy=(2k+1)(2k+1)=4k2+4k+1=2(2k2+2k)+1. Since 2k2+2k is an integer because k is an integer then xy is odd. The proof is correct but the statement is incorrect The statement is correct, but the proof is incorrect. The statement and proof are incorrect. The statement and the proof are correct.
hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.
Odd number integers = 2k + 1, where k is integer
Even number integer = 2k
Odd integer + even integer
= 2k + 1 + 2k
= 4k + 1
= 2(2k) + 1
Let 2k = t, where t is integer
= 2t + 1
= Odd integer by definition
If number is 2t + 1 where t belongs to integer, then it is odd integer.
Hence proved.
The question is incomplete. The complete question is :
Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd
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a newsletter publisher believes that less than 49% of their readers own a personal computer. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.05 level of significance, the advertiser decides to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
The proportion should be sufficiently demonstrated to be lower than 49% at the 0.05 level.
Given,
Less than 49% of a newsletter publisher's subscribers, in their estimation, own a personal computer.
A potential advertiser wants to verify this claim for marketing purposes.
The marketer chooses to reject the null hypothesis after running a test with a 0.05 level of significance.
We have to determine the conclusion regarding the publisher's claim;
Here,
Null and Alternative hypothesis;
H₀ = P ≥ 0.49
H₁ = P < 0.49 (Left tailed test)
The significance level is 0.05
So,
0.05 < 0.49
Then,
At the defined meaning level, it is chosen to reject the null hypothesis.
Therefore,
There should be sufficient evidence that the proportion is lower than 49% at the 0.05 level.
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I need part a and how the answer was made ‼️
Answer:
Step-by-step explanation:
a mouse weighs around 18–35 gram. [ 1] , while an average elephant around 5,443 kilogram. [ 2] Which means an elephant is about 200,000 times heavier then a mouse. (of course, a baby elephant of 100 kilogram compared to a heavy mouse (33 1 3 gram) only weighs 3000 times heavier) Footnotes. [ 1] Species Specific Information: Mouse.
the number of disintegrations per minute (dsm) of a sample of iodine-133 is measured at 5.5 x 102 dsm. when the sample is measured 295 minutes later, the number of disintegrations has decreased to 4.7 x 102 dsm. what is the half-life of iodine-133
Half-life of iodine-133 is 21.7 hours .
FR = 0.5n (fraction remaining)
n = number of half lives that have elapsed.
FR = 4.7x102 / 5.5x102 = 0.8545
n = to find
0.8545 = 0.5n
log 0.8545 = n log 0.5
-0.0683 = -0.301 n
n = 0.227 half lives have elapsed
Since this is equal to 295 minutes, we can easily find what 1 half life is
0.227 / 295 = 1 / x
x = 1300 min = 21.7 hours
The amount of time it takes for the concentration of a given reactant to reach half of its initial concentration is known as the half-life of a chemical reaction (i.e. the time taken for the reactant concentration to reach half of its initial value).
It is commonly expressed in seconds and is represented by the sign t1/2 .
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14 on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
The number of men on the sight - seeing tour was 22 .
In the question ,
it is given that,
the ratio of women to children on the tour is = 5 : 2
let the number of men in the sight seeing tour = m
let the number of women in the sight seeing tour = w
let the number of children in the sight seeing tour = c
So , w/c = 5x/2x
also the ratio of children to men is 5/11 ,
c = 5y and m = 11y
the number of women on the sight seeing tour is less than 30 ,
which is 5x < 30 ,
x < 6
but we have c = 2x and 5y ,
and since c is a multiple of 5 , 2x also has to be a multiple of 5 ,
earlier we got , x < 6 ,
Now using x =5 , we get c = 2*5 = 10
and so , 10 = 5y
y = 2 ,
So , the number of men = 11y = 11*2 = 22 men
Therefore , the number of men are 22 .
The given question is incomplete , the complete question is
On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
(2) The number of women on the sight-seeing tour was less than 30.
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if z is a standard normal variable, find the probability. the probability that z lies between -0.56 and 0.56
The normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution.
The usual normal distribution is then followed by the z variable. A value of the x variable's z variable, also known as the z-score of the x variable, indicates how many standard deviations from the mean it is.
The area under the normal distribution curve must be calculated that lies between
z=−1.56 and z=1.56
Using the standard normal table, the area is calculated as:
P(−1.56<z<1.56)
=P(z<1.56)−P(z<−1.56)
=P(z<1.56)−(1−P(z<1.56))
=0.9406−(1−0.9406)
=0.8812
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The complete question is
if z is a standard normal variable, find the probability. the probability that z lies between -1.56 and 1.56 is
For the following problems, write the equation that is relevant to solve the problem, the values of the variables that you will use in that equation, and a complete sentence stating what your answer to the question is. Your answer must include appropriate units 1. Five and a half years ago, Elena invested $20,000 in a retirement fund that grew at a rate of 2.96% compounded continuously. What is the investment worth today? What was the interest earned for that investment so far? 2. How long will it take for an investment with an annual rate of 2.85% compounded quarterly to double in value? (Doubling time). How long will it take for the same investment to quadruple in value?
Investment worth today is $23520 and interest earned = $3520 on compound interest.
What is compounding interest?
Compound interest is interest calculated on the initial principal, that conjointly includes all of the accumulated interest from previous periods.
Generating "interest on interest" is thought because the power of interest.
Main body:
1)
time = 5.5 years
rate = 2.96%
Principle amount = $20000
Compounding interest = P(1+r/n)^tn
where
n = number of times interest applied per time period
t=number of time periods elapsed
here n = 365
Amount = 20000(1+0.0296/365)^5.5*365
= 20000*1.176
= $23520
hence ,interest earned = $23520 - $20000 = $3520
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a search committee is formed to find a new software engineer. there are 6666 applicants who applied for the position. 1) how many ways are there to select a subset of 1515 for a short list?
The number of ways would be 2.68367259e14 for selecting 15 candidates out of 66 candidates.
What is arrangements ?Generally speaking, an arrangement of objects is just a collection of them. The sequence of the n items has no bearing on the number of "arrangements" that can be made of them (order is significant).
Total Candidates for software engineer = 66
Total Short listed candidates = 15
To find:
Number of 15 Candidates set possible
⁶⁶C₁₅ = [tex]\frac{66!}{51! 15!}[/tex]
After Calculating from calculator we get,
2.68367259e14.
Hence the number of ways would be 2.68367259e14.
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instructor number of failures prof. a 13 prof. b 0 prof. c 11 prof. d 16 what is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
The standard deviation of the sampling distribution is 0.03
Instructor number is calculated as - (failure /100)
Number of failures for instructor A = 13 = 0.13
Number of failures for instructor B = 0 = 0.
Number of failures for instructor C = 11 = 0.11
Number of failures for instructor D = 16 = 0.16
Calculating mean -
Mean(m)
= 0.13 + 0.11 + 0.16) / 3
= 0.4 / 3
= 0.13
Calculating the Standard deviation -
Σ(X - m)² / N - 1
Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.001266
= 0.001266 / 2
= 0.00063343
= √0.00063343
= 0.025168
= 0.03
Complete question -
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?
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Which number sentence shows the best way to estimate 64.12÷7.4 ? A. 60 ÷ 10 = 6 60÷10=6
B. 63 ÷ 7 = 9 63÷7=9
C. 56 ÷ 7 = 8 56÷7=8
D. 100 ÷ 10 = 10
Answer:
B
Step-by-step explanation:
Round 64.12 and 7.4 to whole numbers that divide nicely, and are CLOSE to the original numbers.
Layla is thinking of a positive single digit even number. Luis guesses it was 7. What is the sample space??
The sample space for the single digit even number = {2, 4, 6, 8}
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space.
Events are the subset of possible experiment results. Depending on the experiment, a sample space could contain a variety of results.
Given that,
Layla thinks about a positive single digit even number.
There are four single digit even numbers 2, 4, 6 and 8.
The sample space for the single digit even number = {2, 4, 6, 8}
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Describe the relationship between the lines.
1. The lines intersect to form an angle that is 180°
2. The lines intersect to form an angle that is not 90°
3. The lines intersect to form an angle that is 90°
4. he lines do not intersect.
A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits? choose the equation for the population of rabbits, r, in terms of the number of years that have passed, y, and the correct solution.
When the population starts out with 8 people and triples, it will take 5 years to reach 1,944.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Initial population=8
Final population=1944
Rate of increment=3ˣ
1944=8*3ˣ
1944/8=3ˣ
243=3ˣ
3ˣ=3⁵
x=5
It will take 5 years for the population to reach 1,944 when started with with the population of 8 and increase by 3ˣ.
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A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15°, from a height of 2. 2 feet. How far away does the ball land in feet?use x=(v * cos [theta])*ty=h+(v * sin [theta]t-16t^2Solve T in the second equation using the quadratic formula, then solve x
The ball will land 67.381 feet away.
Thus, option (B) is correct.
Given:
v = 62 feet / second
[tex]\theta[/tex] = 15
h = 2.2 feet
Using the formula
Horizontal range = [tex]\dfrac{v \;cos\; \theta\; [v \;sin\;\theta + \sqrt{v^2\;sin\;\theta + 2gh]}}{g}[/tex]
Substituting the value back into the formula as
Horizontal range = [tex]\dfrac{62 \;cos\; (15)\; [62 \;sin\;(15)+ \sqrt{(62\;sin\;(15))^2 + 2g*2.2]}}{g}[/tex]
= 67.381 feet
Therefore, the distance is 67.381 feet.
Thus, option (B) is correct.
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The question attached here seems to be incomplete, the complete question is:
A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15", from a height of 2.2 feet. How far away does the ball land in feet? (5 points)
56.372 feet
67.381 feet
60.646 feet
47.293 feet
help me out with probability
The probability of selecting D twice in the random selection is D. 4 / 9.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
It should be noted that the probability of selecting D will be:
= 2 / 3.
Therefore, the probability of selecting D twice will be the multiplication of the probability that's gotten twice. This will be illustrated thus:
= 2 / 3 × 2 / 3
= 4 / 9
Therefore, the probability is 4 / 9.
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Choose the expression that is equivalent to the quantity 9 raised to the negative second power times 9 raised to the seventh power end quantity all raised to the negative third power −99 negative 1 divided by 9 raised to the sixth power 1 divided by 9 raised to the fifteenth power 927
The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
How to use the Law of Indices?
We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. Indices display the results of multiples of a number, such as squared or cubed, or they display the roots of numbers, such as the square root. The laws of indices can be used to condense some indexed terms.This is written as;
(9⁻² * 3⁵)⁻²
According to laws of indices, we know that;
(a²)³ = a²*³ = a⁶
Thus;
(9⁻² * 3⁵)⁻²= (9⁻²)⁻² * (3⁵)⁻²
⇒ 9⁴ * 1/3¹⁰
⇒ 9⁴/3¹⁰
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Answer:The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
suppose that a full 3-ary tree has 100 internal vertices. how many leaves does it have? suppose that a full 4-ary tree has 100 leaves. how many internal vertices does it have?
Answer:
i = (L – 1)/(m – 1) = 99/3 = 33. i = 33.
Step-by-step explanation:
Which table could be a partial set of values for a linear function?
Responses
x y table 1
0 0
1 1
2 4
3 9
x y 0 0 1 1 2 4 3 9 , , ,
x y table 2
0 0
1 1
2 8
3 27
x y 0 0 1 1 2 8 3 27 , , ,
x y table 3
0 0.0
1 0.5
2 1.0
3 1.5
x y 0 0.0 1 0.5 2 1.0 3 1.5 , , ,
x y table 4
0 0.0
1 0.5
2 2.0
3 4.5
Answer:
table 3
Step-by-step explanation:
As we know that
A Linear function is the one whose graph represents a line OR value of its dependent and independent variable change at a rate which remains constant throughout.
Now in the fourth table the values of x and y are given as show below:
Leah runs 2000 meters in 5 minutes. How may meters can Leah run in one min
meters per minute
Answer:
Leah runs:
400 meters per minute
Step-by-step explanation:
2000 meters ⇒ 5 minutes
A meters ⇒ 1 minute
A = 2000 meters * 1 minute / 5 minute
A = 400 meters
HELPPP MREEEEEEEEEEEED SLAY
Answer:
l. and ll and lll only
Step-by-step explanation:
Horizontal lines are parallel so as suggested in:
1. Vertical angles are congruent, so 5a = 115.
2. Alternate interior angles are congruent, so b - 12 = 65.
3. Corresponding angles are congruent and linear angle pairs sum up to 180, so (b-12) + 65 = 180.
However, alternate interior angles are congruent,
as stated in 2nd suggestion too, so the sum is not 180 but 130.
Therefore 4th suggestion is not correct.
Cesar danced for 16 minutes on Saturday. On Sunday he danced for 28 minutes more than he did on Saturday. How long has he danced in total
Answer:
60 minutes
Step-by-step explanation:
Saturday = 16 minutes
Sunday = 28 minutes + 16 minutes = 44 minutes
Saturday + Sunday = 44 + 16 = 60 minutes
The length of a rectangular poster is 2 more inches than three times its width. The area of the poster is 161 square inches. Solve for the dimensions (length and width) of the poster.
The length and width of the rectangular poster are 23 inches and 7 inches respectively.
Here we have to find the dimensions of the length and width of the rectangular.
Data given:
length of the rectangular poster is 2 more than three times its width.
Let us assume that the width of the rectangular is x.
The area of the poster = is 161 inches²
So by this, we get the length 3x + 2.
width = x
length = 3x + 2
The formula of the area of the rectangular:
Area = length × width
161 = (3x+ 2) × x
161 = 3x² + 2x
3x² + 2x - 161 = 0
3x² + 23x - 21x - 161 = 0
x(3x + 23) - 7( 3x + 23) = 0
(3x + 23) ( x -7)= 0
x = -23/3, 7
As the length cannot be negative so we get the value of x as 7
width = 7 inches
length = 3x + 2
= 3×7 + 2
= 21 + 2
= 23inches
Therefore the length and width are 23 inches and 7 inches respectively.
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Determine the ratio of the geometric sequence: 1/16, -1/4, 1,...
Answer:
The common ratio of the given sequence is - 4-------------------------------
Given sequence:
1/16, - 1/4, 1, ...Find the common ratio, the ratio of two consecutive terms:
r = 1 ÷ (- 1/4) = 1 × (- 4) = - 4or
r = - 1/4 ÷ 1/16 = - 1/4 × 16 = - 48x-2 < 30 help pls im slow
Answer: x < 4
Step-by-step explanation: look at the link attached
When Angel left his house in the morning, his cell phone battery was partially charged. Let B represent the charge remaining in Angel's battery, as a percentage, t hours since Angel left his house. A graph of B is shown below. Write an equation for B then state the x-intercept of the graph and determine its interpretation in the context of the problem.
The equation of the function is: B = -5x + 30
X-intercept is 6, which means after 6 hours, the battery is totally drained.
What is the X-intercept of a Function?The x-intercept of a function is the point on the x-axis that the line intercepts, which is the value of x when y = 0.
Find the slope of the function (m):
Slope (m) = change in B / change in t = (20 - 10) / (2 - 4)
Slope (m) = 10/-2
Slope (m) = -5
The y-intercept (b) = 30.
Write the equation of the function by substituting m = -5 and b = 30 into B = mt + b:
B = -5x + 30
The x-intercept of the function is 6, which represents the hours it took for the whole battery to drain.
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What is the measure of ZLMQ?
Answer:
97
Step-by-step explanation:
< LMN = 33
The sum of the interior angles equal 180
180 - 92 - 55 = 33
<QM (can't read the last letter 50
180 - 45 - 85 = 50
<LMQ This is a straight angle and straight angles are 180
180 - 33 -50 = 97
Brandon enters bike races. He bikes 6 1/2 miles every 1/2 hour. Complete the table to find how far Brandon bikes for each time interval.
Answer:
Step-by-step explanation:
Your friend simplifies the following problem. Describe what error was made. No credit for just the correct final answer, we are looking for you to tell us what is wrong with how this was solved.
The error was made when he added the number in the radical expression in the computation, despite the fact that the numbers do not have the same base.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The expression is given in the question following:
4√5 + 7√3
11√8
The error was made in that he add the number in the radical expression in the calculation while the terms are not the same base.
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