The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled. help me
Answer:
The height of the water increases 2 inches per minute.
Step-by-step explanation:
the slope is always the ratio of
y coordinate change / x coordinate change
in our case, x is the time (minutes), and y is the water height (inches).
we see, the longer the pool get filled, the higher the water gets. logical, right ?
by checking the data points we see :
with every 2 minutes passing the water height increases by 4 inches.
so, the slope is +4/+2 = 2/1 = 2
and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.
every 2 minutes 4 inches more.
so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.
and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.
Describe the graph of a quadratic function below given in table form
How much for $100 invested in 6% interest compounded monthly be worse after 20 years
Answer:
$331.02
Step-by-step explanation:
compound interest formula
A = P ( 1 + r/n)^nt
P = principal amount
r = rate decimal
n = number of times interest is compounded
t = time
A = 100 * (1 + .06/12)^(12*20)
A = 331.02
A cab company charges a $5 boarding rate in addition to its meter which is $3
for every mile. What is the equation of the line that represents this cab
company's total charge?
Re
co
Answer:
m3+5
Step-by-step explanation:
m is miles
take the number of miles multiply by3
take that answer add 5
The equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
What is an Equation ?A statement that relate two expressions with an equal sign is called an Equation.
It is given that
A cab company charges a $5 boarding
Charges for every mile is $3 per mile
Let x be the mile travelled
The cab's total charge is represented by y
then y = 3x + 5
Therefore the equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
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What are the rational roots of ? x = 1, x = -1 x = 1, x = 0 x = 1, x = 2 This polynomial has no rational roots.
only 1st main ,please do solve this asap
Answer:
(i) 8b-32
(ii) 7z^3+12z^2-20z
(iii) –q+p
(iv) a+ab
(v) 8x^2y+8xy^2-4x^2-7y^2
(vi) 4y^2-3y
Step-by-step explanation:
The following confidence interval is'obtained for a population proportion p: 0.87 < p < 0.93 What is the margin error E. The following confidence interval is'obtained for a population proportion p : 0.87 < p < 0.93 What is the margin error E.
The margin error of the confidence interval 0.87<p<0.93 is 0.03.
Given confidence interval 0.87<p<0.93.
We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.
Confidence interval is 0.87<p<0.93.
Width of the interval= 0.93-0.87
=0.06
=0.03
Hence the margin of error is equal to 0.03.
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forty percent of participants in a math contest were boys. fifty percent of the boys revived medals. the number of boys who received the medals was equal to the number of girls who received the medals. what percent of the participants were girls who received medal?
20% of the participants are girls and got a medal, and 33% of the girls got a medal.
What percent of the participants were girls who received medal?
First, we know that 40% of the participants were boys, so the other 60% were girls.
We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:
P = (0.4)*(0.5) = 0.2
So, 20% of the participants are boys and got a medal.
We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.
Then if the percentage of girls that got a medal is x (in decimal form), we must have that:
Q = (0.6)*(x) = 0.2
x = 0.2/0.6 = 0.33
x = 0.33
This means that 33% of the girls got a medal.
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On a coordinate plane, a parabola opens down with solid circles along the parabola at (negative 3, negative 5), (negative 2, 0), (negative 1, 3), (0, 4), (1, 3), (2, 0), (3, negative 5). Which statement is true regarding the intervals where the function is increasing and decreasing? The function is increasing from (–∞, 0). The function is increasing from (0, ∞). The function is decreasing from (–∞, 0). The function is decreasing from (–∞, ∞).
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
On a coordinate plane, a parabola opens down with solid circles along the parabola at (-3, -5), (-2, 0), (-1, 3), (0, 4), (1, 3), (2, 0), (3, -5).
The domain is all real numbers.
The range is all real numbers.
If for an interval I, when x decreases meanwhile staying in interval I, the function's output increases (or can stay same), then we say that the function is increasing in the interval.
The true statement regarding the intervals where the function is increasing and decreasing is option A: The function is increasing from (–∞, 0).
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Answer:
A
Step-by-step explanation:
17, 18, 22, 31, 47 what is the next number
Answer:
the next number is 47+ 16 =63
A condominium is taxed based on its $78,584 value. The tax rate is $3.49 for every $100 of value. If the tax is paid before March 1, 4%
of the normal tax is given as a discount. How much tax is paid if the condominium owner takes advantage of the discount?
The tax paid by the condominium owner is $2,632.88.
What is the tax paid?
Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.
Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.
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The table displays the scores of students on a recent exam. Find the mean of the
scores to the nearest 10th.
Score Number of Students
70
7
75
5
80
4
85
1
90
6
Answer:
78.7
Step-by-step explanation:
To find the mean, we can do the sum of all scores divided by the total amount of scores.
We see that there are 7 scores of 70, and 70*7=490.
We see that there are 5 scores of 75, and 75*5=375.
We see that there are 4 scores of 80, and 80*4=320.
We see that there is 1 score of 85, and 85*1=85.
We see that there are 6 scores of 90, and 90*6=540.
Now we can do [tex]\frac{490+375+320+85+540}{7+5+4+1+6} =\frac{1810}{23} =78.7[/tex]
1) When the polynomial P(x) is divided by x+5, the remainder is 3. Which of the following is definitely true?
a) P(3) = 5
b) P(-5) = 3
c) P(5) = 3
d) P(-3) = 5
2) P is a degree 3 polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i. What is the other zero?
a) 4-3i
b) 4+3i
c) -5
d) 3-4i
1) The definitely true for the statement is b) P(-5) = 3.
2) The three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
What is the remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
Given;
1) When the polynomial P(x) is divided by x+5, the remainder is 3.
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder will be P(-5).
So, P(-5) = 3
Therefore, the definitely true for the statement is b) P(-5) = 3.
2) P is a 3 degree polynomial with real coefficients and three zeros. Two of the zeros are 5 and 3+4i.
The complex roots always exist in conjugate pairs so,
3 + 4i and 3 - 4i
Thus, the three roots are 5, 3 + 4i, and 3 - 4i. Option D is correct.
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help please
what is
Answer:
sure how can I help you? please tell me
If anyone can help me to solve this.
Answer:
1) x + 96 = 90°
2) x + 89 = 80°
Step-by-step explanation:
Consecutive Interior Angles Theorem
When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line. Each pair of consecutive interior angles are supplementary (sum to 180°).
Question 1To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 96)° + (x + 96)° = 180°
⇒ x + 96 + x + 96 = 180
⇒ 2x + 192 = 180
⇒ 2x + 192 - 192 = 180 - 192
⇒ 2x = -12
⇒ 2x ÷ 2 = -12 ÷ 2
⇒ x = -6
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 96 = -6 + 96 = 90°
⇒ x + 96 = 90°
Question 2To find the measure of the angle circled on the diagram, find the value of x by using the Consecutive Interior Angle Theorem:
⇒ (x + 109)° + (x + 89)° = 180°
⇒ x + 109 + x + 89 = 180
⇒ 2x + 198 = 180
⇒ 2x + 198 - 198 = 180 - 198
⇒ 2x = -18
⇒ 2x ÷ 2 = -18 ÷ 2
⇒ x = -9
Substitute the found value of x into the expression to find the measure of the angle circled on the diagram:
⇒ x + 89 = -9 + 89
⇒ x + 89 = 80°
Answer:
[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]
Step-by-step explanation:
Part 1 :
x + 96 + x + 96 = 180 (angle pairs of a line)2x + 192 = 1802x = -12x = -6∠ = -6 + 96∠ = 90°Part 2 :
x + 109 + x + 89 = 180 (same reason)2x + 198 = 1802x = -18x = -9∠ = -9 + 89∠ = 80°14)
Given a circle with a radius of 5, which equation expresses it as the ratio of the circumference of a circle to its diameter?
A)
B)
C)
D)
sin
- 7
10
216
C
Answer: 10
Step-by-step explanation: The diameter is twice the radius
Suntract (7x-3x)-(5x-6).
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]
[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]
[tex]\qquad \tt \rightarrow \: - x + 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:6-x
Step-by-step explanation:
The solution is in the image
What is the surface area of prism below?
Answer:
Aprism = 483.246 yd2
Step-by-step explanation:
The surface area is the sum of the 2 circles areas and the rectangle area.
Ac1 = PI*r2
Ac1 = (3.14)*(11.4/2)2
Ac1 = 102.0186 yd2
Ac1 = Ac2 then
Ac2 = 102.0186 yd2
Now the perimeter of the circle is one the sides of the rectangle:
Pc = 2PI*r
Pc = 2*3.14*(11.4/2)
Pc = 35.796 yd
Now the area of the rectangle is:
Ar = 7.8yd*35.796yd
Ar = 279.2088 yd2
Then, the surface area of prism is:
Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism = 483.246 yd2Mark divided a basket of apples evenly into small bags. The number of bags was equal to the number of apples in each bag. Which could be the total number of apples?
A. 25 B. 27 C. 20 D. 18
There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.
What is a Perfect Square ?A perfect square is a number which can be written as the product of an integer with itself.
It is given that Mark divided a basket of apples evenly into small bags.
Let there be n no. of bags and therefore n number of apples in each bag
Then the total number of apples will be
n * n
n²
The value of total number of apples should be a perfect square,
In the option given only 25 is the perfect square
Therefore the equation can be made as
n² = 25
n = 5
There are 5 bags and each bag has 5 apples and total there are 25 apples.
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Which of the function correctly expresses the exponential model f(x)=6(14)^x with base of e
The exponential equation with a base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
How to change the base?
We start with:
[tex]f(x) = 6*(14)^x[/tex]
We want to rewrite this to:
[tex]f(x) = 6*(e^n)^x[/tex]
So we only need to find the value of n such that:
[tex]e^n = 14[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]
Then the exponential equation with base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
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PLEASE GIVE STEP BY STEP EXPLANATION !!
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): A graph with two linear functions; f of x passes through 0, negative 1 and 5, 14, and g of x passes through negative 6, negative 1 and negative 1, 14. Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points) Part B: Solve for k in each type of transformation. (4 points) Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The two types of transformations that can be used to transform f(x) to g(x). g (x) = f(x) + 16 and g (x) = f(x + 8)
ABC has vertices at A (12, 8), B (4, 8)
What is the equation about?f(x)= 0, -1 ,5,14
g(x)= -6, -1, -1, 14
g(x)=f(x)+k
-6= 0+k
k= -6
A) g (x) = f(x) + 16 and
g(x) = f(x + 8)
B) g(x)=f(x)+k
-1= -1+ k
k= -1+1=0
g(x)=f(x)+k
-1= 5+k
k= -1-5=-6
g(x)=f(x)+k
14= 14+k
k= 0
k= -6,0,-6,0
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In formula P = 2L + 2W
A. solve for L
B. solve for W
C. Find P if L=12 and W=8
Answer:
P=2l+2W
if l=12 and W=8
then,
P=2L+2W
=2.18+2.8
=36+16
=52
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked
at random. What is the probability that the counter is green or purple? Give
your answer as a fraction.
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.
The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).
So the probability of selecting a green or purple counter is:
Probability = (Number of green counters + Number of purple counters) / Total number of counters
Probability = (7 + 1) / 11
Probability = 8/11
Therefore, the probability of selecting a green or purple counter is 8/11.
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The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage
Answer:
I think it's 80%
Step-by-step explanation:
Method 1: (40/50)*100 = 80%
Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%
The students in Mr. McIntyre’s class and the students in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.
Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
Which statement correctly compares the means of the data in the dot plots?
The correct statement compares the means of the data in the dot plots is option C; the mode is greater for Mrs. Ramos’s class.
What are the median and mode of the data?Median represents the middle value of the given data when arranged in a particular order.
Mode is that number that appears most frequently in the given set of data.
Given;
The Number of pets in Mr. McIntyre’s class ;
0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,
Median = 1
Mode = 0 and 1
The Number of pets in Mrs. Ramos’s Class;
0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3
Median = 3
Mode = 4 and 5
Hence, C; The mode is greater for Mrs. Ramos’s class.
The remaining part of the question is
"Which statement correctly compares the measures of center of the data in the dot plots?
The median is greater for Mr. McIntyre’s class.
The median is the same for both classes.
The mode is greater for Mrs. Ramos’s class.
The mode is the same for both classes."
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Please help I’m confused
Answer:
Step-by-step explanation:
radical 5* radical 2
Answer:
[tex] \sqrt{10} [/tex]
Step-by-step explanation:
Rule: [tex] \sqrt{a} \times \sqrt{b} = \sqrt{ab} [/tex]
[tex] \sqrt{5} \times \sqrt{2} = \sqrt{5 \times 2} = \sqrt{10} [/tex]
Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown.
x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8.
8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12.
The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong?
The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly.
The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Total Questions = 20
Total Points = 28
Correct Answers = +2 points
Incorrect Answers = -1 point
The viewer represents the correct answers with x and the incorrect ones with y.
x+y = 20
for every correct answers 2 points;
and for every incorrect answers, -1 point
This can be written as
2x-y = 28
The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;
now
2x-y = 28
x+y = 20
On adding the equations
]3x = 48
x = 16
y = 4
This means that the contestant answered 16 questions correctly and 4 questions incorrectly
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.
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Another day, another math problem 2
Answer:
-7
Step-by-step explanation:
you can use power rule of derivatives for that.
Find the value of the function f(x) = x2 + 9x + 10, for x = -1.
Answer:
this is pretty easy we just replace the x with -1 so
(-1)^2+(-1)9+10
-1*-1=1
-1*9=-9
1+-9=-8
-8+10=2
f(-1)=2
Hope This Helps!!!
