There's seven-eighths of a gallon of chocolate ice cream in the freezer. There's also two-thirds of a gallon of vanilla ice cream.
[tex]\frac{7}{8}[/tex] gallons of chocolate ice-cream
[tex]\frac{2}{3}[/tex] gallons of vanilla ice-cream
To find how much more chocolate ice cream is there than vanilla
We subtract vanilla from chocolate
[tex]\frac{7}{8} -\frac{2}{3}[/tex]
To subtract fractions we make the denominators same
least common denominator is 24
[tex]\frac{7*3}{8*3} -\frac{2*8}{3*8}[/tex]
[tex]\frac{21}{24} -\frac{16}{24}[/tex]
[tex]\frac{5}{24}[/tex]
[tex]\frac{5}{24}[/tex] of a gallon
A family of four spent 104 dollars for tickits at a concert all the tickits were the same price price was the cost of each ticket
To find the cost of each concert ticket for a family of four, divide the total cost, $104, by the number of tickets, which is 4. The resulting cost per ticket is $26.
The student is asking for help with a simple division problem. A family purchased concert tickets for a total of $104, and we know there are four tickets purchased since it's a family of four. To find the cost of each ticket, we have to divide the total cost ($104) by the number of tickets (4).
Step-by-Step Solution:
Determine the total spent: $104.
Determine the number of tickets: 4.
Calculate the cost per ticket: $104 ÷ 4 = $26.
Therefore, the cost of each concert ticket was $26.
A uniform distribution is defined over the interval from 6 to 10.
a. what are the values for a and b?
b. what is the mean of this uniform distribution?
c. what is the standard deviation?
d. show that the total area is 1.00 (use the area formula)
e. find the probability of a value more than 7 f. find the probability of a value between 7 and 9
Answer:
Refer below
Step-by-step explanation:
a) a and b are the lower and higher values of the interval for which uniform distribution is defined.
Here a= 6 and b =10
b) Mean of the uniform distribution= (a+b)/2 = (6+10)/2 =8
Or int x (1/4) dx = x^2/8 = 8
c) Variance of the uniform distribution = (b^2-a^2)/12 = (100-64)/12
= 36/12 =3
Std dev = sq rt of 3 = 1.732
d) To find total area
PDF of the distribution = 1/(b-a) = 1/4, 6<x<10
Area = \int 6 to 10 of 1/4 dx
= x/4
Subtitute limits
= (10-6)/4 =1
So total area = 1
d)P(X>7) = int 7 to 10 of 1/4 dx = 3/4
e) P(7<x<9) = Int 7 to 9 of 1/4 dx = 2/4 = 1/2
Probabilities are used to determine the chances of events
The values of a and b
The interval is given as 6 to 10.
So, the values of a and b are 6 and 10, respectively.
The mean
For a uniform distribution, the mean is:
[tex]\bar x = \frac{a + b}{2}[/tex]
So, we have:
[tex]\bar x = \frac{6 + 10}{2}[/tex]
[tex]\bar x = 8[/tex]
Hence, the mean is 8
The standard deviation
For a uniform distribution, the standard deviation is:
[tex]\sigma = \sqrt{\frac{b^2 - a^2}{12}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{10^2 - 6^2}{12}}[/tex]
[tex]\sigma = 2.31[/tex]
Hence, the standard deviation is 2.31
The total area
This is calculated as:
[tex]A = \int\limits^b_a \frac{1}{b - a}\ dx[/tex]
So, we have:
[tex]A = \int\limits^{10}_6 \frac{1}{10 - 6}\ dx[/tex]
[tex]A = \int\limits^{10}_6 \frac{1}{4}\ dx[/tex]
Factor out 1/4
[tex]A = \frac{1}{4}\int\limits^{10}_6 \ dx[/tex]
Integrate
[tex]A = \frac{1}{4} * x|\limits^{10}_6[/tex]
Expand
[tex]A = \frac{1}{4} * (10 - 6)[/tex]
[tex]A = 1[/tex]
Hence, the total area of the distribution is 1.00
The probability of a value more than 7
This is calculated as:
[tex]P(x > 7) = \frac{1}{4} * x|\limits^{10}_7[/tex]
Expand
[tex]P(x > 7) = \frac{1}{4} * (10 - 7)[/tex]
[tex]P(x > 7) = 0.75[/tex]
Hence, the probability of a value more than 7 is 0.75
The probability of a value between 7 and 9
This is calculated as:
[tex]P(7 < x < 9) = \frac{1}{4} * x|\limits^9_7[/tex]
Expand
[tex]P(7 < x < 9) = \frac{1}{4} * (9 - 7)[/tex]
[tex]P(7 < x < 9) = 0.50[/tex]
Hence, the probability of a value between 7 and 9 is 0.50
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The dashed triangle is a dilation image of the solid triangle. what is the scale factor?
A. 1/4
B. 1/2**
C. 2/3
D. 2?
Will give 25 points. and brainliest.
Which polynomial represents the area of the rectangle?
the table shows realtionships betweeen.....
B. is the graph that fills the requirements
Graph2 with slope of 25 is the graph that shows the relationship on the table.
How to determine the graph of a set of dataTo find the equation of the line passing through points A(3, 75) and B(12, 300) follow these steps:
1. Calculate the slope m:
m = (y₂ - y₁)/x₂ - x₁)
m = (300 - 75)/(12 - 3)
m = 225/9
m = 25.
Graph2 with same slope as the calculated slope is the graph that shows the relationship on the table.
2. Use the point-slope form with one of the points (e.g., A(3, 75)
y - y₁ = m(x - x₁)
y - 75 = 25(x - 3)
3. Simplify the equation:
y - 75 = 25x - 75.
4. Isolate y
y = 25x.
So, the equation of the line passing through points A(3, 75) and B(12, 300) is y = 25x
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Need help asap please! Which equation matches the graph shown?
A.Y=x^2-6x+2
B.Y=2x^2-4x+2
C.Y=x^2-2x+1
D.Y=-2x^2+4x-2
Answer:
The correct option is A.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex] ..... (1)
Where, (h,k) is vertex and a is a constant.
From the given graph it is clear that the vertex of the graph is (3,-7) and y-intercept is (0,2).
Substitute h=3 and k=-7 in equation (1).
[tex]y=a(x-3)^2-7[/tex]
The y-intercept is (0,2). So, substitute c=0 and y=2 in the above equation to find the value of a.
[tex]2=a(0-3)^2-7[/tex]
[tex]2+7=a(3)^2[/tex]
[tex]9=9a[/tex]
Divide both sides by 9.
[tex]1=a[/tex]
The value of a is 1.
Substitute a=1, h=3 and k=-7 in equation (1).
[tex]y=1(x-3)^2-7[/tex]
[tex]y=x^2-6x+9-7[/tex]
[tex]y=x^2-6x+2[/tex]
The equation of the parabola is [tex]y=x^2-6x+2[/tex].
Therefore the correct option is A.
Select the action you would use to solve x/4 =16. Then select the property that justifies that action
Answer:
Given equation is:
x/4 = 16
Multiply both side of equation by 4
4* x/4 = 16*4
x= 64
Step-by-step explanation:
This is called Multiplication property of Equality.
If you multiply equation by a number on both sides, it remain same or balance.
The equation x/4 =16 is solved by multiplying both sides by 4, resulting in x = 64. This action is justified by the Multiplication Property of Equality.
Explanation:To solve the equation x/4 =16, the action one would use is to multiply both sides of the equation by 4. This operation will isolate the variable 'x'.
Your equation would thus be transformed as: 4 * (x/4) = 16 * 4. This simplifies to x = 64.
The property that justifies this action is the Multiplication Property of Equality, which states that multiplying both sides of an equation by the same non-zero number does not change the equality.
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Write a division equation that has a solution of -20
Final answer:
A division equation that has a solution of -20 can be written by dividing a negative number by a positive number, such as -100 divided by 5.
Explanation:
To write a division equation with a solution of -20, you can choose any two numbers such that the division of one number by the other equals -20. For example, if we take -100 and divide it by 5, we get -20 as the solution. Thus, a sample division equation could be:
-100 / 5 = -20.
This is because when you divide a negative number by a positive number, the result is negative, and -100 \/ 5 leads to the desired solution of -20.
Solve the equation. If there is no solution, write no solution. Y + 8 – 2(y – 20) > 0
Which rule describes the x-coordinates in the translation below?.
x + 0
x + 6
x – 6
x + 2
Answer:
A) x + 0
Step-by-step explanation:
In triangle ABC, the coordinates are: A(1, -1), B(1, -5) and C(4, -5)
In triangle A'B'C', the coordinates are: A(1, -5), B(1, 1) and C(4, 1)
Look at the x-coordinates in both the triangles remains the same because the triangles are reflected over x-axis, therefore, only the y-coordinate changes.
Therefore, the rule for x-coordinates = x + 0
Answer: A) x + 0
Hope this will helpful.
Thank you.
Answer:a
Step-by-step explanation:
the tax rate is 6.8%
what is the tax on $9.95
round to the nearest hundredth (explain your answer)
The tax on a $9.95 purchase with a 6.8% tax rate, rounded to the nearest hundredth, is approximately $0.68.
Explanation:To calculate the tax on a purchase, you can multiply the purchase amount by the tax rate. In this case, $9.95 is being multiplied by 6.8% (or by 0.068 as a decimal). So, the calculation would look like this: $9.95 * 0.068 = $0.6766. However, the question asks to round to the nearest hundredth. So, the final tax would be approximately $0.68.
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A family of 2 adults and 3 children go to a play. Admission cost $8 per adult and $5 per child what expression would show the total admission cost for the family
answer=2X8+3X5=16+15=31
∠C and ∠D are vertical angles with m∠C=−3x+58 and m∠D=x−2 . What is m∠D ? Enter your answer in the box
∠C and ∠D are vertical angles
so <C = <D because vertical angles are equal
Substitute
−3x + 58 = x−2
Solve for x
Subtract x from both sides
-4x + 58 = - 2
Subtract 58 from both sides
-4x = - 60
Divide both sides by -4
x = 15
<D = x−2 = 15 - 2 = 13
Answer
<D = 13°
Answer:
The measure of angle D is 13°
Step-by-step explanation:
-3x+58=x-2
+3x to each side
58=4x-2
Add 2 to each side
60=4x
Divide each side by 4
X=15
Now substitute that in:
-3(15)+58=13
(15)-2=13
The measure of angle D is 13°
What is the quadratic equation of the curve of best fit shown below
what is the x-intercept of the line with this equation 8x - 1/3y = 15?
Isolate the x. Note the equal sign. What you do to one side, you do to the other. First, add 1/3y to both sides
8x - 1/3y (+1/3y) = 15 (+1/3y)
8x = 15 + 1/3y
Divide 8 from both sides
(8x)/8 = (15 + 1/3y)/8
x = 15/8 + 1/24y
x = 1/24y + 1.875
x = 1/24y + 1.875 is your answer
hope this helps
HELPP!!! Will give Brainliest!!!
What is the local maximum value of the function? (Round answer to the nearest thousandth.) g(x) = 3x^3 + 3x^2 - 30x + 24
Answer:
The answer is 72.578 :))
Step-by-step explanation:
I got it right in my exam
You can peel 4 potatoes in 10 mintues . How long will it take you to peel 14 potatoes?
40 mins is the answer
10 mins-4
20mins-8
30mins-12
40mins-16
which ratios are equivalent to 3 parts silver paint to 4 parts green paint?
Answer:
6:8, 9:12
Step-by-step explanation:
Answer:
6:8 9:12
Step-by-step explanation:
Find the amount in an account if $3,500 is invested at 6.12% compounded monthly, for 4.5 years
Answer:
4606.48 $
Step-by-step explanation:
Amount invested P = 3500 $
Rate of interest r = 6.12%
Compounding monthly
Monthly rate of interest = 6.12/12 =0.51%
Time = 4.5 years = 4.5 (12) = 54 months
Hence final amount would be
P(1+0.01r)^t
Here r = 0.51 and t = no of months = 54
Hence final amount
= 3500(1.0051)^54
= 3500(1.31613)
=4606.48 $
Thus 3500 if invested now will become 4606.48 in 4.5 years at the rate of interest of 6.12% compounding monthly.
Factor the expression over the complex numbers.
x^2 + 20
Using complex numbers, you can have negative squares, since [tex] i^2=-1 [/tex]
So, you can find the solutions to
[tex] x^2+20=0 \iff x^2 = -20 \iff x=\pm\sqrt{-20}=\pm i \sqrt{20}=\pm 4i\sqrt{5} [/tex]
So, using the factorization [tex] (x-x_1)(x-x_2) [/tex] where [tex] x_{1,2} [/tex] are the roots of the quadratic equation, you have
[tex] x^2+20 = (x-4i\sqrt{5})(x+4i\sqrt{5})[/tex]
This expression can't be further factorized, because all terms have degree 1.
To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.
Explanation:To factor the expression x^2 + 20 over the complex numbers, we can use the quadratic formula or complete the square.
Using the quadratic formula, we start by finding the values of x that satisfy the equation x^2 + 20 = 0.
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, a = 1, b = 0, and c = 20. Substituting these values into the quadratic formula, we get: x = ± √-20.
Since we are factoring over the complex numbers, we can express the solution as: x = ± √20i.
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Find the product 1.9(8.43)
help! What does this mean??
3 radical 7 - radical 7
= 3
why is this incorrect?
Algebraically, you have to factor the square root of 7 to see why you're wrong:
[tex] 3\sqrt{7}-\sqrt{7} = \sqrt{7}(3-1) = 2\sqrt{7} [/tex]
Conceptually, think that any object - say an apple - represents the square root of seven.
So, you have three apples, and you take away one apple. You have two apples remaining, i.e. [tex] 2\sqrt{7} [/tex]
[tex]3\sqrt{7} - \sqrt{7}[/tex]
Let x represent [tex]\sqrt{7}[/tex], then you can rewrite the expression as 3x - x.
3x - x = 2x. Now replace "x" with [tex]\sqrt{7}[/tex] and you get 2[tex]\sqrt{7}[/tex].
The reason 3 is incorrect is because you are supposed to perform the operation (+, -, x, ÷) with the coefficients, not with the variable or radical.
What is the axis of symmetry and vertex for tge function f(x)=3(x-2)
If you distribute the multiplication, your function is written as
[tex] y=f(x)=3x-6 [/tex]
Like every function in the form [tex] y = mx+q [/tex], this function represents a line. A line has no vertex and no axis of symmetry (actually, it is symmetric with respect to every perpendicular line).
(X^2-3)(x^2+3x-1) multiply the polynomials
x^2 - 3(x^2 + 3x - 1)
Distributive property.
x^4 + 3x^3 - x^2 - 3x^2 - 9x + 3
Combine like terms.
x^4 + 3x^3 - 4x^2 - 9x + 3
Mary and Joe are trying to save money for a trip this summer. Mary start with $10 and earns $10 each week mowing lawn. Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds. How many weeks will it take for Mary and Joe to have the same amount saved
ANSWERS
Find out the how many weeks will it take for Mary and Joe to have the same amount saved.
To proof
Let us assume that the number of week take for Mary and Joe to have the same amount saved be x.
As given
Mary start with $10 and earns $10 each week mowing lawn.
Joe already has $20 from birthday gifts and earns five dollars a week pulling weeds.
than the equation
10 + 10x = 20 +5x
5x = 10
x = 2 weeks
therefore 2 weeks will it take for Mary and Joe to have the same amount saved.
Hence proved
Which expression represents a quadratic expression in complete factored form?
A.)(2x+4)(x-3)
B.)(x-1)(3x-9)
C.)(x+4)(x-3)
D.)(x-2)+(x+3)
Answer: C
Step-by-step explanation:
A) not completely factored because 2 can be factored out of 2x + 4
B) not completely factored because 3 can be factored out of 3x - 9
C) CORRECT
D) not factors because the terms are added instead of multiplied
Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.
What is a Quadratic equation?It is a polynomial of maximum power 2. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
Which expression represents a quadratic expression in complete factored form?A. (2x + 4)(x - 3)
On multiplying
2x² - 2x -12
B. (x - 1)(3x - 9)
On multiplying
3x² -12x + 9
C. (x + 4)(x - 3)
On multiplying
x² + x - 12
D. (x - 2) + (x + 3)
On multiplying
2x + 1
Thus, (x - 2) + (x + 3) is not a quadratic equation. Then A, B, and C are the quadratic equation.
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What is the area of a triangle whose vertices are R(−4, 2) , S(1, 2) , and T(−5, −4) ?
Enter your answer in the box.
________ units²
That triangle has a horizontal base with y=2. The length of that base is RS=1-(-4)=1+4=5. The height of the triangle is the vertical distance from line y=2 to T(-5,-4). That height is 2-(-4)=2+4=6. The area of the triangle is base * height/2 = 5*6/2= 15
The answer is 15 units ^2
Answer:
The answer is 15 units².
Step-by-step explanation:
I am a hundred percent sure. I did the math and got it right on my test.
Which answer choice best describes f(x) = x - 12?
A. The relationship shows a direct linear variation with a constant variation of-12.
B. The relationship shows a direct linear variation with a constant of variation of 12.
C. The relationship shows a direct linear variation with a constant variation of 1.
D. The relationship does not show a direct linear variation.
D
a direct linear variation equation has the form f(x) = kx
f(x) = x - 12 is not in this form thus does not show a direct linear variation
Can someone help me on this
I know that i had it on a test its -2.11 Hope you ace it!
-2.11 hope this helps
A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number. The letters and numbers can repeat. Note: there are 26 letters in the alphabet. How many different license plates can be made? Answer plates what is the probability of getting a plate with abc123 or 123abc? P(abc123 or 123abc) = answer (enter as a reduced fraction using / for the fraction bar.)
The number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A license plate has six characters. Three characters are letters, two characters are numbers (0-9), and one character is a letter or a number.
Total letters = 26
Total numbers = 10
As the repetitions are allowed.
Number of ways = 26×26×26×10×10×(26+10)
N=63,273,600 Ways
P(abc123 or 123abc) = P(abc123)+P(123abc) - P(abc123 and 123abc)
The intersection of abc123 and 123abc is zero because both license plates are not possible at a time
P(ABC123 or 123ABC)=P(ABC123)+P(123ABC)
[tex]\rm P=\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}\dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8} + \dfrac{1}{10}\dfrac{1}{9}\dfrac{1}{8}\dfrac{1}{26}\dfrac{1}{25}\dfrac{1}{24}[/tex]
P= 2/5616000
or
P = 1/2,808,000
Thus, the number of different license plates that can be made is 63,273,600 and the probability of getting a plate with abc123 or 123abc is 1/2,808,000.
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