If a polynomial is divisible by another then that will be a factor of the polynomial. The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8.
What is an algebraic factor?An algebraic factor is the multiplication of two algebraic terms.
That term could be in the form of summation multiplication or in subtraction.
The root of the quadratic equation formed by the algebraic factor is always real.
As per the given polynomial,
p(x) = 4x³ + cx² + x + 2
Divide 4x³ + cx² + x + 2 by (x+2)
First quotient = 4x²
Then, (4x³ + cx² )- (4x³ + 8x²)
Now in order to become it zero c must be the same as 8.
c = 8
Then, the second quotient = 1
(x + 2) - (x + 2) = 0
So, 4x³ + cx² + x + 2 = (x + 2)(4x² + 1)
Hence "The value of c such that the given polynomial p(x) = 4x³ + cx² + x + 2 is divisible by (x + 2) is 8".
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There are five people competing in the track meet this weekend. They are competing for 1st, 2nd, and 3rd place ribbons. How many different ways can the winners be chosen? A. 30 B. 60 C. 120 D. 150
If they are competing for 1st, 2nd, and 3rd place ribbons. The number of different ways can the winners be chosen is: B. 60.
How to find the total possibilities?Given data:
Number of people =5
Number of places = 1st, 2nd, and 3rd
Hence,
Different combinations =5 ×4×3
Different combinations = 60 ways
Therefore the winners will be chosen by 60 different possible ways ,
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Determine which of the lines, if any, are parallel or perpendicular. explain. line a passes through (2, 10) and (4, 13). line b passes through (4, 9) and (6, 12) . line c passes through (2, 10) and (4, 9) .
Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Line a passes through (2, 10) and (4, 13). So, the slope of this line is
[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]
Line b passes through (4, 9) and (6, 12). So, the slope of this line is
[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]
Line c passes through (2, 10) and (4,9). So, the slope of this line is
[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]
The product of slopes of perpendicular lines is -1.
and if the slope of 2 lines is equal then those lines are parallel
so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
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A box of volume 216 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost. (use symbolic notation and fractions where needed. write the objective function with respect to the length of the square bottom.)
The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m are equal to .
How to find the height of the box ?Let h is the height of the box.
Given Volume of the box is 216 m³ with no top.
And the cost of the bottom is 40USD/m².
For the sides, it is 30USD/m².
The bottom of the box is square, so l = w.
So Volume
[tex]V=hl^{2}[/tex]
[tex]216=hl^{2}[/tex]
[tex]h=\frac{216}{l^{2} }[/tex]
Now Surface Area of the box without a top is
S = 4hl + l²
So,
cost = 4 × 30hl +40l²
cost = 120 hl + 40 l²
Putting h ,
cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]
cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]
To find minimum cost, derivate the by using the calculator at
[tex]l=3\sqrt[3]{4}[/tex]
l=4.762203 m
[tex]h=\frac{216}{4.762203^{2} }[/tex]
h = 9.5244069354 m
Hence the dimensions of the box are
l=w
=9.52 m
and height ,h=3.17 m
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the p-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. we conclude that this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 what type of error is possible here?
The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.
What is Type 1 error and Type 2 error?When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.
When we feel to reject a false H₀ it is known as type 2 error.
H₀:P= 0.12
Hₐ:P= 0.12
The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.
Therefore, it only suggests that there is a possibility that we will make a type 1 error.
Consequently, Type 1 error is the response to our query.
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Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?
The required expression which is equivalent to -51 -(-60) is -51 + 60.
Given that,
Which expression is equivalent to -51 - (-60) is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression = -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60
Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.
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Stacy is one-fourth as old as her mother. If Stacy's mother is 36, how old is Stacy?
Answer: Stacy is 12 years old
Step-by-step explanation:
36/4 = 12
9. A family ordered 2 large pizzas for lunch. They ate
7
-
8
of one pizza and of the other pizza. What
fraction of a pizza was left for dinner?
118
b. 1/2
d. 12/12
b.
e.
318
334
C.
718
00
10
Answer:
9/16
Step-by-step explanation:
in a survey, 19 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $40.7 and standard deviation of $9.2. estimate how much a typical parent would spend on their child's birthday gift (use a 80% confidence level). give your answers to 3 decimal places.
The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
A sample mean is the result of a chance experiment. When we sample a random variable, we get one of its possible values. A sample is a specific value. The random variable's probability distribution determines the possible values and the likelihood of each.
Given that,
Point estimate = sample mean = X = 40.7
sample standard deviation = s = 9.2
sample size = n = 19
Degrees of freedom = df = n - 1 = 19 - 1 = 18
At 80% confidence level
α = 1 - 80%
α =1 - 0.80 =0.2
α/2 = 0.1
t α/2,df = t0.1,18 = 1.330
The margin of error = E = t /2, df x (s/√n)
= 1.330 x (9.2/√19)
= 1.330 x 2.110
= 2.8
Margin of error = E = 2.8
The 80% confidence interval estimate of the population mean is,
X ± E
= 40.7 ± 2.8
= (43.5, 37.9)
Therefore The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
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Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.
The number of ways voters could rank their first 5 choices out of 10 is 30240.
Given,
Number of students sought the nomination for president of the student body = 10 students
We have to find the number of ways voters could rank their first 5 choices.
Permutation;
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here we have to use permutation formula;-
ⁿPr = n! / (n - r)!
Here,
n is the number of students = 10
r is the choices = 5
Then,
ⁿPr = n! / (n - r)!
¹⁰P₅ = 10! / (10 - 5)!
¹⁰P₅ = 10! / 5!
¹⁰P₅ = 10 x 9 x 8 x 7 x 6
¹⁰P₅ = 30240
That is,
The number of ways voters could rank their first 5 choices out of 10 is 30240.
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street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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Point B is graphed on the coordinate plane. Which ordered pair represents point B?
a school has 400 grade 9's, 375 grade 10's, 300 grade 11's and 325 grade 12's. twenty students from each grade are surveyed
The type of bias that can be present in stratified sampling is that the students cannot be selected to accurately reflect the population.
How are samples classified?Samples may be classified according to the five options as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, an equal amount of students from each class was surveyed, hence a stratified sample was used.
The type of bias present in stratified sampling is that the students cannot be selected to accurately reflect the population.
Missing InformationThe problem asks for which type of bias is present in this sample.
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he management of an indoor shopping mall wants to survey its shoppers about the layout of the stores in the mall. at a specified time one day, they send a team of interviewers to survey 2 randomly selected customers in each of the 48 stores in the mall. this scenario describes
The scenario describes the stratified random sampling method .
There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .
Stratified Random Sampling : It is a method of sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .
Therefore , the scenario describes the stratified random sampling method .
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Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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15 POINTS HELP!
A liquid used to unclog sinks has a pH value of 14. This liquid is _____.
neutral
an acid
a base
Answer:
A base
Step-by-step explanation:
its not an acid bc a ph level of 14 means is has a strong base.
Suppose m<4 =108 find m<5 and m<7
m ∠5 and m ∠7 is 72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or π (in radians).
How to find angle ?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
m ∠4 = 108°
m ∠5 = m ∠1
m ∠1 is in same line of m ∠4
So
m ∠1 = 180 - m ∠4
m ∠1 = 180 - 108
m ∠1 = 72 °
So m ∠5 = 72 °
m ∠7 is opposite to m ∠5 , opposite angles will be equal
Therefor m ∠7 = 72 °
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Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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help meeeeeeeeeeeeeeeeee please
Answer:
324 ft
Step-by-step explanation:
[tex]v=\sqrt{2gh}[/tex]
[tex]v^2=(\sqrt{2gh})^2[/tex]
[tex]v^2=2gh[/tex]
[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]
[tex]\frac{v^2}{2g}=h[/tex]
[tex]\frac{144^2}{2(32)}=h[/tex]
[tex]\frac{20736}{64}=h[/tex]
[tex]324=h[/tex]
What would the final cost be
for a trick or treat bucket that
originally costs $3.00 if you
have a coupon for 10% off and
you have to pay tax of 7.5%?
Answer:
4.73
Step-by-step explanation:
10% is 10
so, you have to multiple 3×.10=.30
3-.30=2.70
2.70×.75 because 7.5% is .75
that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73
Hope that works
Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
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the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
What is probability?The area of mathematics known as probability deals with numerical representations 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, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.learn more about probability click here:
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26% of all college students major in stem (science, technology, engineering, and math). if 36 college students are randomly selected, find the probability that a. exactly 7 of them major in stem. b. at most 10 of them major in stem. c. at least 7 of them major in stem. d. between 9 and 15 (including 9 and 15) of them major in stem.
The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.
let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .
as per the statement 26% students are major in stem
total students selected randomly are 36.
∴ P(S) = 0.26
P( F) = 1 - 0.26 = 0.74
Now the binomial probability of success is given by
[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]
where C is for the combination formula
S is changes of success
F is chances of failure
x = no. of times success
n = total times the experiment done
From the provided information we can solve each case as follows :
A) exactly 7 of them major in stem
P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]
= 0.1081
B)at most 10 of them major in stem
it means P(0,1,2...10)
∴ P = P(0) + P(1) +......+P(10)
P = 0.676
C) at least 7 of them major in stem.
it means P(7,8,9...36)
∴ P = P(7) + P(8) + ...+ P(36)
P = 0.863
D) between 9 and 15 (including 9 and 15) of them major in stem.
In this case we subtract P(0,1,2...8) from P(0,1,2,...15)
and get P(9,10,11,...15)
∴ P(9,10,11,...15) = P(0,1,2,...15) - P(0,1,2...8)
= 0.987 - 0.382
= 0.605
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F(x)=-2x-3 find f(-1)
Answer:
x = -1
Step-by-step explanation:
mark me on brainliest please follow me to
Answer:
-1
Step-by-step explanation:
Replace the variable x with 1 in the expression .
f(1)= 2(1) - 3
Remove the parenthasis
2(1) - 3
Multiply 2 by 1
2 - 3
subtract 2 from 3
-1
heidi's scores on her first 3 tests were 92, 95, and 86. what is the minimum score she mulst earn on her next test to maintain at least a 90 average
The inequality that needs to be solved is:
3t +270/ 6 ≥ 90.
let we consider that Heidi has 6 subjects in her school.
Therefore, She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.
Now,
To obtain an average first add up all the scores of the tests and then divide by the number of tests.
So far Heidi has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.
If we let each of the three remaining tests each be represent by t, then the sum of all the tests would be:
95 + 92 + 86 + t + t + t
or
273 + 3t
The average of these 6 tests can then be represented by:
3t + 273 / 6
And for her average to be at least 90 then she can get a 90 or more which is the same as ≥ 90
So the inequality that needs to be solved is:
[tex]\frac{3t + 273}{6}[/tex] ≥ 90
or, [tex]\frac{3 ( t + 91)}{6} \geq 90[/tex]
or, [tex]\frac{t + 91}{2} \geq 90[/tex]
Now, Heidi has to score :
t/2 ≥ 91
or, t/2 ≥ 90
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please help me with this math problem
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The value of function is positive so the function have maximum value 30 at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value 30 at x=3.
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Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.
B. ∠CBA ≌ ∠DBA by CPCTC.
What is the SAS Congruence Theorem?The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other
When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.
Part A:
We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.
Also, AB ≌ AB based on the reflexive property.
Therefore, both triangles are congruent to each other based on SAS.
ΔABC ≌ ΔABD
Part B:
Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.
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Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 0,10, with ten being the happiest. A line was fit to the data to model the relationship.
Answer:
The answer is B. y = -x + 7.5.
Step-by-step explanation:
The slope is -1 and the y-intercept is 7.5.
PLEASE MARK AS BRAINLIEST!!!Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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