Answer: [tex]\frac{5}{36}[/tex]
Step-by-step explanation:
Given
dice with Prime number is rolled
The number on the face of dice are 2,3,5,7,11 and 13
Probability of getting a product of 4 is [tex]\frac{1}{36}[/tex]
Now probability of getting product has a unit digit one is possible when outcome is
[tex](3,7),(7,3),(13,7),(7,13),(11,11)[/tex]
i.e. there are 5 favorable outcomes
So probability is [tex]\frac{5}{36}[/tex]
Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select three options. The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.
Answer:
The vertex of the function is at (–3,–16)
The graph is increasing on the interval x > –3
The graph is positive only on the intervals where x < –7 and where x > 1
Step-by-step explanation:
The roots of this function are the values that make f(x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = -7
The x-coordinate of the vertix can be calculated as:
x_v = (x1 + x2)/2 = -6/2 = -3
So the first statement: "The vertex of the function is at (–4,–15)" is wrong.
The y_coordinate of the vertex is:
f(x_v) = (x_v - 1)*(x_v + 7) = (-3 -1) * (-3 +7) = (-4) * (4) = -16
So the second statemente: "The vertex of the function is at (–3,–16)" is correct.
for values of x greater than x_v = -3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.
As the roots are 1 and -7 and the concavity is upwards, the parabola have positive values for x<-7 and x>1. So the fourth statement is correct.
For values of x< -4, the parabola can have both positive or negative values (it has positive values for x < -7) so the fifth statement is wrong.
Answer:
B. The vertex of the function is at (–3,–16).
C. The graph is increasing on the interval x > –3.
D. The graph is positive only on the intervals where x < –7 and where
x > 1.
Polynomials - Guided Notes 11.2
Part 1: Find the degree of the polynomial.
1. 3x + 2
2. 4x3 + 17x - 5
3. 13x" + 5xn-2
4. 0.55x2 + 0.7x
5. 7x3 + 10x + 15
Answer:
1. 3x + 2 - First degree
2. 4x3 + 17x - 5 - Third degree
3. 13x" + 5xn-2 - Second degree
4. 0.55x2 + 0.7x - Second degree
5. 7x3 + 10x + 15 - Third degree
Step-by-step explanation:
The degree of a polynomial is given by the highest power of the given variable (x in this case) in the polynomial. All the elements are considered in selecting the highest power of x in the polynomials.
Considering all; the highest degree of x in the polynomials given is 3 while the lowest is 1 hence we have polynomials ranging from the first to third degrees.
Find the surface area of the prism. Write your answer as a decimal.
Answer:
1.5cm³
Step-by-step explanation:
Surface area of a prism = bh x 6
0.5 x 0.5 = 0.25 x 6 = 1.5
Answer:
1.5 cm
Step-by-step explanation:
a=6a^2
a=6(0.5)^2
a=6(0.25)
a=1.5 cm
Max travles to see his brother 's family by car. He drives 216 miles in 4 hours what is his rate in miles per hour use a double nuber line to show your work
Answer: 54 miles per hour
Step-by-step explanation:
Max travles to see his brother 's family by car and he drives 216 miles in 4 hours. To calculate his rate in miles per hour, we divide the amount of distance he travelled by the number of hours used. This will be:
Distance= 216 miles
Time taken= 4 hours
Speed = Distance travelled/Time taken
= 216/4
= 54 miles per hour
Which correctly compares 4.06 and 4.6?
A) 4.6 < 4.06
B) 4.6 = 4.06
C) 4.06 > 4.6
D) 4.06 < 4.6
Answer:
B is your answer
Step-by-step explanation:
Final answer:
The correct comparison is that 4.06 is less than 4.6 because when looking at the decimal parts, '0.6' (4.6) is greater than '0.06' (4.06).
Explanation:
To compare the numbers 4.06 and 4.6, we need to look at the decimal parts, since the whole number part (4) is the same for both. In the number 4.06, the decimal part is '06', which is actually '0.06' when read as a fraction of the whole number. On the other hand, 4.6 has a decimal part of '6', which is '0.6' as a fraction of the whole number. When comparing '0.6' and '0.06', it is clear that '0.6' is larger because '6' tenths is greater than '6' hundredths.
Therefore, the correct comparison between 4.06 and 4.6 is 4.06 < 4.6, which corresponds to option D in the question.
Help...i dont know how to solve this
X^2- 64
Answer:
x = ±8
Step-by-step explanation:
X^2- 64
Set this equal to 0
x^2 -64 =0
Add 64 to each side
x^2-64+64 = 64+64
x^2 = 64
Take the square root on each side
x = ±sqrt(64)
x = ±8
Answer:
Step-by-step explanation:
a²-b²=(a+b)(a-b)
x²-64=x²-8²
=(x+8)(x-8)
Alice had 3 1/4 pounds of flour at the beginning of the week. At the end of the week, she had 2 3/4 pounds. How much has she used?
The amount of flour alice had used at the end of the week is;
Amount = ¹/₂ pounds
Amount of flour she had at the start of the week = 3¹/₄ pounds
Amount she had at the end of the week = 2³/₄ pounds
To solve this, we need to first covert the mixed fractions to improper fractions.Thus;
3¹/₄ pounds = 13/4 pounds
2³/₄ pounds = 11/4 pounds
Thus,
amount of flour she used = amount at the start of week - amount left at end of week
Amount of flour she used = 13/4 - 11/4The denominator is the same and so our solution is to just subtract the numerator and retain the common denominator. This gives;
Amount of flour she used = ¹/₂ pounds
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What is 10.9544 rounded to the nearest tenth
:D
Answer:
10.95
Step-by-step explanation:
anything under 4 rounds down and anything over 4 rounds up. so your answer would be 10.95
10.9544 rounded to the nearest tenth would be 11.0. When rounding to the nearest anything, remember to look at the number to the right of it. If it is greater or equal to five, round up. If the number is less than five, round down. In this situation, the number to the right of "9" (the position of the tenth) is five, which means we should round up, which would equal 11.
I hope this helped -- if it did, please thank, rate, and mark as brainliest! If you have any more questions or concerns, feel free to ask! Thank you, stay safe, and have a great rest of your day/quarantine! (i know it's hard, but we're almost through. we've got it!)
f an investor puts $1500 dollars into an account at an annual rate of 4.8% interest compounded twice a month, how much will they have after two years?
Answer:
They will have $1651 after two years.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
$1500 dollars into an account at an annual rate of 4.8%
This means that [tex]P = 1500, r = 0.048[/tex]
Interest compounded twice a month.
A year has 12 months.
So 12*2 = 24 compundings, which means that [tex]n = 24[/tex]
How much will they have after two years?
This is A(2).
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(2) = 1500(1 + \frac{0.048}{24})^{24*2} = 1651[/tex]
They will have $1651 after two years.
A computer is sold for a certain price and then its value changes exponentially over time.
The graph describes the computer's value (in dollars) over time (in years).
value (dollars)
500
400+
300+
5
200+
100+
time
(years)
0.5
1
1.5
2
2.5
3
3.5
How does the computer's value change over time?
Answer: the computer loses 50% of its value each year
Step-by-step explanation:
The diameter of the base of a come measures 8 units. The height of the cone is 6 units. What is the volume of the cone in terms of pie
Answer:
Step-by-step explanation:
diameter = 8 units
r = 8/2 = 4 units
h = 6 units
[tex]Volume=\frac{1}{3}\pi r^{2}h\\\\=\frac{1}{3}*\pi*4*4*6\\\\[/tex]
= π*4*4*2
=32π cubic units
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.
Question:
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of $114.00. Assume the population standard deviation is $15.30. Construct a 90% confidence interval for the population mean.
Answer:
At the 90% confidence level, confidence interval = 110.2484 < μ < 117.7516
At the 95% confidence level, confidence interval = 109.53 < μ < 118.48
The 95% confidence interval is wider
Step-by-step explanation:
Here, we have
Sample size, n = 45
Sample mean, [tex]\bar x[/tex] = $114.00
Population standard deviation, σ = $15.30
The formula for Confidence Interval, CI is given by the following relation;
[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]
Where, z is found for the 90% confidence level as ±1.645
Plugging in the values, we have;
[tex]CI=114\pm 1.645 \times \frac{15.3}{\sqrt{45}}[/tex]
or CI: 110.2484 < μ < 117.7516
At 95% confidence level, we have our z value given as z = ±1.96
From which we have [tex]CI=114\pm 1.96 \times \frac{15.3}{\sqrt{45}}[/tex]
Hence CI: 109.53 < μ < 118.48
To find the wider interval, we subtract their minimum from the maximum as follows;
90% Confidence level: 117.7516 - 110.2484 = 7.5
95% Confidence level: 118.47503 - 109.5297 = 8.94
Therefore, the 95% confidence interval is wider.
Answer:
B. is the correct option.
With 90% the population mean price is
in lies in (127.01,134.99). With 95% confidence, it can be said that the population mean price lies in ( 126.24,135.76)
Therefore, the 95% confidence interval is wider than 90%.
The calculation is attached
Tom has a cube a rectangle prism and a triangular prism. Which of these shapes have more than 6 vertical?
The cube and rectangular prism.
Step-by-step explanation:
The triangular prism has 5 and the other two both have 8.
None of the shapes mentioned in the question, a cube, a rectangular prism, or a triangular prism, have more than six faces. For more complex shapes like Icosahedron, they do carry more than six faces.
Explanation:The student's question is about understanding which among the shapes - a cube, a rectangular prism, and a triangular prism - has more than six faces. To answer this, we should first understand that a cube and a rectangular prism (or cuboid) both have 6 faces and a triangular prism also has 5 faces only. Hence, none of these shapes deliver more than 6 faces as specified in the question. For a three-dimensional shape to have more than 6 faces, one has to move towards more complex shapes. For example, the provided reference suggests Icosahedron, a shape with 20 faces is an example of a shape with more than six faces.
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Which angle is congruent to angle AGC
what is 32.5 cents as a decimal
Answer:
32.5
Step-by-step explanation:
its a trick question
A recipe calls for 1 1/4 cups of sugar for every 3 cups of flour. How much sugar would be needed for 5 cups of flour?
Answer:
[tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour
Step-by-step explanation:
Number of cups of sugar required for 3 cups of flour =[tex]1 \frac{1}{4}[/tex]
Number of cups of sugar required for 3 cups of flour = [tex]\frac{5}{4}[/tex]
Number of cups of sugar required for 1 cup of flour [tex]=\frac{\frac{5}{4}}{3}[/tex]
Number of cups of sugar required for 5 cups of flour =[tex]\frac{\frac{5}{4}}{3} \times 5[/tex]
Number of cups of sugar required for 5 cups of flour =[tex]\frac{25}{12}[/tex]
Number of cups of sugar required for 5 cups of flour =[tex]2\frac{1}{12}[/tex]
Hence [tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour
What is the y-intercept when f(0)=6^0
Answer:
(0,1)
Step-by-step explanation:
Any real number to the power of 0, including 6, is equal to 1. Therefore, f(0) is 1, and the y intercept is (0,1). Hope this helps!
Solve tan^2 (x) + 3 = 0 for 0 ≦ x < 360∘
Express your answer in degrees. Select the appropriate response
A) 360
B) 180
C) 60
D) None of the above
Help please!!!
Answer:
d) none of the above
Step-by-step explanation:
correct me if wrong .
Final answer:
The equation tan^2(x) + 3 = 0 has no real solutions within the given range.
Explanation:
To solve the equation tan^2(x) + 3 = 0, we need to isolate the term with the tangent squared. Subtracting 3 from both sides gives us tan^2(x) = -3. Since the tangent function is positive for angles between 0° and 360°, it is not possible for the square of the tangent to be negative. Therefore, there are no real solutions to this equation, given the specified range of 0 ≦ x < 360°. So, the correct answer is (D) None of the above.
Complementary, Supplementary, Vertical, and Adjacent Angles
100 POINTS
Answer:
The first picture is A
The second picture is 21.8
The third picture is 20
The fourth picture is B
Step-by-step explanation:
4x + 8x = 180
12x = 180
x = 15
90 - 68.2 = 21.8
7x + 10 = 150
7x = 140
x = 20
Angle A = 63
180 - 63 = 117
Answer:
The first picture is A
The second picture is 21.8
The third picture is 20
The fourth picture is B
Step-by-step explanation:
hope this helps
X/3 - 2 + 6 what is the answer
Answer:
[tex]\frac{x}{3}[/tex]+4
Step-by-step explanation:
I don't think it can be simplified more than that
Answer:
x= -12
Step-by-step explanation:
x/3 -2+6 =0
x/3 +4 =0
x/3 = -4
x/3 (3) = -4 (3)
x = -12
Need this answered today, will give brainliest: The Steelers are on the Cowboys’ fifteen-yard line. Use your place value mat or number line to calculate how
much farther the Steelers need to travel to score a touchdown.
Answer: 15 yards
Step-by-step explanation:
From the question, we have been informed that the Steelers are on the Cowboys' fifteen-yard line. Using the place value mat to calculate how much farther Steelers need to travel to score a touchdown goes thus:
Since the play is 15 yards from the Cowboys end-zone, therefore Steelers need to travel 15 yards for them score a touchdown.
Final answer:
The Steelers are 85 yards away from the end zone.
Explanation:
To calculate how much farther the Steelers need to travel to score a touchdown, we need to know the distance from the Cowboys' fifteen-yard line to the end zone. The distance between each yard line on a football field is 10 yards. Since the Steelers are on the fifteen-yard line, they are 85 yards away from the end zone (100 yards - 15 yards = 85 yards).
The Smiths spend 10% of their budget on entertainment. Their total budget this year is $3,000 more than last year, and this year they plan to spend $5,000 on entertainment. What was their total budget last year?
Answer:
$47,000
Step-by-step explanation:
Let u represent the unknown amount of budget
10/100× u = $5000
10u/100=$5000
Cross multiply both sides
10u= $500000
Divide both sides by the coefficient of u
10u/10=$500000/10
u= $50000
Therefore, this year's budget is $50000
Since Smith's budget this year is $3000 greater than last year's budget, to find last year's budget we simply subtract the difference from this year's budget.
$50000- $3000
= $47000
Thus, Smith's total budget for last year was $47000.
Answer: $47,000
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Their total budget this year is $3,000 more than last year, so we have to add 3000 to their total budged of last year (x). x+3000
Since they spend 10% of their budget on entertainment, we have to multiply the previous expression by the percentage in decimal form (divided by 100).
(x +3000) 10/100 = (x+3000) 0.1
Finally, that expression must be equal to the amount that they will spend in entertainment this year (5000).
(x + 3000) 0.1 =5000
Solving for x:
x+3000 = 5000/0.1
x +3000= 50,000
x = 50,000-3,000
x = $47,000
Feel free to ask for more if needed or if you did not understand something.
Which algebraic expression has like terms?
9 n cubed minus 2 n + 3 minus 4 n squared
7 n cubed + 3 n minus 3 minus 6 n squared
7 n cubed + 4 n minus 3 n cubed minus 5 n squared
6 n cubed minus 4 n Superscript 4 Baseline + 6 n minus 5 n squared
Answer:
The answer is c I think
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
I took test and got 100%
What is the amplitude of the function below?
1
2
(pi)
2(pi)
Answer:
B. 2
Step-by-step explanation:
on Edg2020
Answer:
B. 2 got it right
Step-by-step explanation:
After simplifying the following rational expression, what is the leading coefficient in the NUMERATOR? [Recall: writing in Standard Form]
Answer:
x
Step-by-step explanation:
We are required to simplify the rational expression:
[tex]\dfrac{4}{x^2+4x-5} -\dfrac{5}{x^2-25}[/tex]
First, we factorize the denominators where possible
[tex]x^2+4x-5=x^2+5x-x-5=x(x+5)-1(x+5)=(x-1)(x+5)\\x^2-25=x^2-5^2 \\$Applying difference of two squares\\x^2-5^2=(x-5)(x+5)[/tex]
Therefore, our rational expression becomes:
[tex]\dfrac{4}{(x-1)(x+5)} -\dfrac{5}{(x-5)(x+5)}\\$Taking LCM\\=\dfrac{4(x-5)-5(x-1)}{(x-1)(x-5)(x+5)}\\=\dfrac{4x-20-5x+5}{(x-1)(x-5)(x+5)}\\=\dfrac{-x-15}{(x-1)(x-5)(x+5)}\\$Factoring out minus in the numerator and -(x-5)=(5-x)\ in the denominator\\=\dfrac{x+15}{(x-1)(5-x)(x+5)}[/tex]
Therefore, the leading coefficient of the numerator is x.
plz solve this question.its urgent
Look at the attached picture
Hope it will help you...
Good luck on your assignment
~pragya
What is the measure of angle BCD?
A. 25º
B. 40º
C. 140º
D. 155º
Answer:
c.140
Step-by-step explanation:
Answer:
C. 140 degrees
Step-by-step explanation:
Help me with the two again
Part A:
s = k + 4
Part B:
s = 13 + 4
s = 17
Therefore, Sylvia's age is 17 when Katie is 13.
Use the order of operations to find the value of the expression.
12÷2*3-(7-5)
O A.0
O B.6
O C.16
O D.19
Answer:
C. 16
Step-by-step explanation:
12÷2×3−(7−5) = 16.
I hope this helps!
Following the order of operations (PEMDAS/BODMAS), the expression simplifies as:- 12 ÷ 2 * 3 - (7 - 5) = 6 * 3 - 2 = 18 - 2 = 16. So, the value is 16.
To find the value of the expression 12 ÷ 2 * 3 - (7 - 5), we need to follow the order of operations, often remembered using the acronym PEMDAS (or BODMAS):
1. Parentheses (or Brackets): First, we evaluate what's inside the parentheses. In this case, (7 - 5) equals 2.
2. Exponents (or Orders): There are no exponents or orders in this expression.
3. Multiplication and Division: After dealing with parentheses, we move from left to right. So, 12 ÷ 2 * 3 is calculated as follows:
12 ÷ 2 * 3 = 6 * 3 = 18
4. Addition and Subtraction: Again, we move from left to right. Now we subtract 2 (the result from step 1) from 18 (the result from step 3):
18 - 2 = 16
So, the final answer is 16.
In summary, using the order of operations, the expression simplifies to 16. It's crucial to follow these rules to ensure that mathematical expressions are evaluated correctly, as different orders can lead to different results.
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A college president says, "More than two-thirds of the alumni support my firing of Coach Boggs." The president's statement is based on 200 emails he has received from alumni in the past three months. The college's athletic director wants to perform a test of H0: p = ⅔ versus Ha: p > ⅔, where p = the true proportion of the college's alumni who favor firing the coach. Check if the conditions for performing the significance test are met. Random? No, volunteer response sample
A. Random? No, volunteer response sample Large Counts? Yes
B. Random? Yes Large Counts? fails
C. Both fails
D. Random? Random sample of 100 students Large Counts? np0 = 100(0.13) = 13 ≥ 10 and n(1-p0) = 100(0.87) = 87 ≥ 10