Answer:
1/3
Step-by-step explanation:
[tex]|\Omega|=30\\|A|=10\\\\P(A)=\dfrac{10}{30}=\dfrac{1}{3}[/tex]
Find the equation of the parabola with its focus at (–7,6) and its directrix at y = 4
The equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.
How to illustrate the equation?By drawing the graph, it's can be depicted that the equation in this scenario is x² + 14x + 54.
Complete the square on the expression. This will be done by adding 49. This will be:
= x² + 14x + 7² + 54 - 49
= (x + 7)² + 5
Therefore, the equation of the parabola with its focus at (–7,6) and its directrix at y = 4 will be (x + 7)² + 5.
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given lim x→0 f(x)=4. what is lim x→0 1/4 [f(x)]^4?
Given that
[tex]\displaystyle \lim_{x\to0} f(x) = 4[/tex]
we can use the properties of limits to show
[tex]\displaystyle \lim_{x\to0} \frac14 f(x)^4 = \frac14 \lim_{x\to0} f(x)^4 = \frac14 \left(\lim_{x\to0} f(x)\right)^4 = \frac14 \times 4^4 = 4^3 = \boxed{64}[/tex]
Let's see
[tex]\\ \rm\Rrightarrow \lim_{x\to 0}\dfrac{1}{4}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\lim_{x\to 0}f(x)^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{4}\times 4^4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{256}{4}[/tex]
[tex]\\ \rm\Rrightarrow 64[/tex]
can someone help me with these questions, don’t mind the answers written already
Answer:
a) x value is -2, min is -3(if thats y)
b) x value is 3, max is 21(if thats y)
Step-by-step explanation:
yes you do quadratic formula and such :)
If f(x) = 5x, what is fr¹(x)?
Answer:
The first one
Step-by-step explanation:
The age of A is five years more than that of B. 5 years ago, the ratio of their ages was 3:2. Find their present ages.
Answer:
a: 20
b : 15
Step-by-step explanation:
3*5 = 15
2*5 = 10
15-10 = 5
15+5 = 20
10+5 = 15
Answer:
Let:
Present age of B be 'x' years. Present age of A be ( x + 5 ) years.[tex] \: [/tex]
5 years ago,
Age of A = (x + 5) - 5 years = x years.Age of B = ( x - 5 ) years.[tex] \: [/tex]
According to the question,
[tex] \quad [/tex][tex] \quad [/tex][tex] \quad [/tex][tex]{ \large{ \rm{ \frac{x}{x - 5} = \frac{3}{2} }}} [/tex]
[tex]{ \green{ \implies}}{ \sf{2x = 3(x - 5)}}[/tex]
[tex]{ \green{ \implies}}{ \sf{2x = 3x - 15}} [/tex]
[tex]{ \green{ \implies}}{ \sf{3x - 2x = 15}} [/tex]
[tex]{ \green{ \implies}}{ \sf{x = { \boxed{ \pink{15}}}}} [/tex]
[tex] \: [/tex]
Therefore,
Present age of B (x) = 15 years.
Present age of A (x + 5) = 20 years.
How can you represent writing a check of$10 as an integer
Answer:
Step-by-step explanation:
La cantidad numérica es donde escribes la cantidad del cheque con números/dígitos. Escribe los dólares en forma numérica y luego indica los centavos después del punto decimal. En el ejemplo a continuación, los dólares son ciento veinticinco (125) y los centavos son setenta y cinco (. 75).
A beverage company produces cans of lemonade. According to the label a can contains a volume of 375mL of lemonade. A consumer group tested this claim by measuring the volume of lemonade in 2,500 cans. They found that the volume was normally distributed with a standard deviation of 5mL and a mean of 372mL.
If a can is chosen at random, find:
P (its volume is ≥382mL)
The probability that the volume of a can chosen at random is ≥382 is 0.47725
Normal distribution probabilityProbability is the likelihood or chance that an event will occur. For the given question, we need to calculate the z value as shown;
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Given the following parameters
[tex]x=382mL\\\mu (mean)=372mL\\\sigma(S.D)=5mL[/tex]
Substitute
[tex]z=\dfrac{382-372}{5} \\z=\dfrac{10}{5}\\ z=2[/tex]
In order to calculate the probability that the volume of a can chosen at random is ≥382, we will look for (z≥2)
z≥2 according to probability table is equivalent to 0.47725
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The data in this table represents the production of frozen dessert in millions of gallons per month. This data was then graphed in a Bar Graph. Which statement describes why the Bar Graph is not properly drawn? A. The number of desserts represented by each bar is incorrect. B. The intervals along the vertical axis are unequal. C. Not all of the types of frozen desserts are represented in the Bar Chart. D. The width of the bar representing Regular Ice Cream is more than the width of the other bars.
The statement that describes why the Bar Graph is not properly drawn is D. The width of the bar representing Regular Ice Cream is more than the width of the other bars.
What is a bar graph?A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths that are proportional to the values that they represent.
Here, the width of the bar representing Regular Ice Cream is more than the width of the other bars.
A bar graph plots data using rectangular bars or columns that represent the total amount of observations in the data for that category.
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Which of these is not a possible r-value?
A. 1.2
B. -0.1
OC. 0.5
D. -0.75
Answer:
A) 1.2
Step-by-step explanation:
R can never be greater than 1
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Four hundred seventy-six thousandths as a decimal number.
Answer:
.467
Step-by-step explanation:
467 thousandths are moving the decimal to the front and putting the numbers to the right, so it would be 0.467.
NEED HELP,THANKS!!!!!!!
Answer:
I think it is 3.750
Step-by-step explanation:
Serena constructed a wire barrier to protect her tomato plant from squirrels. The barrier is 2.5 feet from the tomato plant in every direction.
Which statement describes the shape of the barrier?
A.
a circle with a radius of 5 feet
B.
a square with diagonals 5 feet long
C.
a circle with a diameter of 5 feet
D.
a square with sides 5 feet long
The shape of the barrier is a a circle with a diameter of 5 feet.
What is a circle?
A circle is a bounded figure which points from its center to its circumference is equidistant. The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the circumference of the circle.
If all points from the flower is 2.5 feet, it means that the barrier has the shape of a circle.
Diameter = radius x 2
2.5 x 2 = 5 feet
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What is the total number of different 10-letter arrangements that can be formed using the letters in the word FORGETTING?
Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are repeating elements, with the number of times given by [tex]n_1, n_2, \cdots, n_n[/tex], the number of arrangements is given by:
[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:
[tex]A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200[/tex]
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A table of data is given.x(-2,-1,0,1,2)f(x)(71,13,3,0.6,0.1) which exponential model best represents the data
The equation of the exponential model is f(x) = 3 * 0.2^x
How to determine the exponential model?The table of data is given as:
x(-2,-1,0,1,2)
f(x)(71,13,3,0.6,0.1)
An exponential model is represented as:
f(x) = ab^x
When x= 0 and f(x) = 3;
We have:
ab^0 = 3
This gives
a = 3
When x= 1 and f(x) = 0.6
We have:
ab^1 = 0.6
This gives
ab = 0.6
Substitute 3 for a
3b = 0.6
Divide both sides by 3
b = 0.2
Substitute b = 0.2 and a =3 in f(x) = ab^x
f(x) = 3 * 0.2^x
Hence, the equation of the exponential model is f(x) = 3 * 0.2^x
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7. a hockey arena has 10 920 seats. the first row of seats around the rink has 220 seats. the number of seats in each subsequent row increases by 16. how many rows of seats does the arena have?
The number of rows in the arena is 26
How to determine the number of rows?The hockey arena illustrates an arithmetic sequence, and it has the following parameters:
First term, a = 220Sum of terms, Sn = 10920Common difference, d = 16The number of rows (i.e. the number of terms) is calculated using:
[tex]S_n = \frac{n}{2}(2a + (n -1) * d)[/tex]
So,we have:
[tex]10920 = \frac{n}{2}(2 * 220 + (n -1) * 16)[/tex]
Evaluate the terms and factors
[tex]21840 = n(440 + 16n -16)[/tex]
Evaluate the like terms
21840 = n(424+ 16n)
Expand
21840 = 424n + 16n^2
Rewrite as:
16n^2 + 424n - 21840 = 0
Using a graphical tool, we have:
n = 26
Hence, the number of rows in the arena is 26
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A garden supply store sells two types of lawn mowers.Total sales of mowers for the year were $8379.79. The total number of mowers sold was 30. The small mower costs $249.99. The large mower costs $329.99. Find the number of large mowers sold.
a.
11
c.
17
b.
19
d.
9
Please select the best answer from the choices provided
A
B
C
D
Answer:
value + value = 8379.70
249.99x + 329.99*30-329.99x = 8379.70
-80x + 9899.70 = 8379.70
-80x = -1520.00
x = 19
30-x = 11
Step-by-step explanation:
Solve -32x + 3 < 5.
A. > 3 and x < 3
OB. > -3 and x < 1
OC. x > 3 or x ≤ 1
Answer:
Negative one over 6
Step-by-step explanation:
you must download mathspapa
and write that number to solve it
Kerri has a germen shepherd that has a mass of 30,000 grams. how many kilograms is 30,000 grams
Write a rule to describe the transformation
Transform this equation to slope-intercept form: 6x + 4y = 8.
O y=3/2x+4
○ y=-3/2x+4
○ y =3/4 x+2
○y=-3/2x+2
Answer:
last option
Step-by-step explanation:
[tex]6x + 4y = 8 [/tex]
[tex]4y = 8 - 6x[/tex]
[tex]y = \frac{8 - 6x}{4} \\ [/tex]
[tex]y = \frac{8}{4} - \frac{6x}{4} \\ [/tex]
[tex]y = 2 - \frac{3x}{2} \\ [/tex]
[tex]y = - \frac{ 3x}{2} + 2 \\ [/tex]
y = -3/2x + 2
The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 4 feet tall and 6 feet wide
The Pythagorean theorem also known as the Pythagoras' theorem, is the basic relationship between the three sides of a right triangle. The length of the diagonal of the screen is 7.211 ft.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the diagonal is 4 feet tall and 6 feet wide. Therefore, using the Pythagorean theorem, The length of the diagonal of the screen can be written as,
[tex]\text{Length of the diagonal} = \sqrt{4^2+6^2} = \sqrt{52} = 7.2111\rm\ ft[/tex]
Hence, the length of the diagonal of the screen is 7.211 ft.
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Circle P has a circumference of approximately 75
inches.
a
What is the approximate length of the radius, ? Use
3.14 for T. Round to the nearest inch.
O 12 inches
O24 inches
O38 inches
O46 inches
Answer:
l think the answer is 024 inches because it has to division
Step-by-step explanation:
just divide both sides by 3.14 yes
The radius of the circle is 12 inches.
What is the radius?Radius is the distance from the center of the circle to any point on its circumference, which means the line segment that connects the center of a circle to any point on its circumference is called the radius.
Given that the circumference of a circle is 75 inches we need to find the radius,
So,
C = π × diameter
75 = 3.14 × d
d = 23.88
∵ d = 2r
∴ r = 23.88/2
r = 11.94
r ≈ 12
Hence the radius of the circle is 12 inches.
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Pretest: Unit 8
Question 12 of 13
Which option below provides the best description of the relationship between
a quadratic parent function and a square root parent function?
A. The square root function is the quadratic function reflected across
the y-axis.
B. The square root function is the quadratic function reflected across
the line y = x, with a limited domain.
C. The square root function is the quadratic function reflected across
the x-axis.
The square root function is the quadratic function reflected across.
We have given that,
a quadratic parent function and a square root parent function
A. The square root function is the quadratic function reflected across
the y-axis.
B. The square root function is the quadratic function reflected across
the line y = x, with a limited domain.
C. The square root function is the quadratic function reflected across
the x-axis.
We have to determine the correct option.
What is the parent function?
A parent function is the simplest function of a family of functions that preserves the definition of the entire family.
The correct option is,
B. The square root function is the quadratic function reflected across.
the line y = x, with a limited domain.
graph y=x^2 and y=√x and y=x
graph is attached
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Which inequality's graph will have a dashed boundary line?
A.
x + 7y > 3
B.
7x + y ≤ 3
C.
6x − 5y ≥ 4
D.
y − x ≤ 3
An inequality that will have dashed boundary line will be separated by a less than < or greater than > sign. From the option given, the correct inequality is x + 7y > 3
Graph of inequalitiesInequalities are expression not separated by an equal sign. According to the question, we ned the inequality's graph that will have a dashed boundary line.
An inequality that will have dashed boundary line will be separated by a less than < or greater than > sign.
From the option given, the correct inequality is x + 7y > 3
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Which operations is the following set closed under? Explain your answer. \(\left\{2,4,6,...\right\}\)
The operation that is being used to complete the sequence is an addition, in which each number is added + 2.
What is a sequence?A sequence is a mathematical term that refers to the succession of numbers or other mathematical objects related to each other, which is characterized by taking into account the relative position of each number with respect to the previous one.
According to the above, it can be inferred that from the following sequence:
2, 4, 6, ...The operation that is defining the sequence is:
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Answer:The operation that is being used to complete the sequence is an addition, in which each number is added + 2.
What is a sequence?
A sequence is a mathematical term that refers to the succession of numbers or other mathematical objects related to each other, which is characterized by taking into account the relative position of each number with respect to the previous one.
According to the above, it can be inferred that from the following sequence:
2, 4, 6, ...
The operation that is defining the sequence is:
x + 2
0 + 2 = 2
2 + 2 = 4
4 + 2 = 6
Step-by-step explanation:
Simplify:
7x³ + 5x² -2 = [?]
X=-1
Answer: - 4
Step-by-step explanation:
Since x is already given, which is -1, just substitute the value.
7 * -1 * -1 * -1 + 5 * -1 * -1 - 2
7 * -1 + 5 * 1 - 2
-7 + 5 - 2
-2 - 2 = - 4
Which of the following sets of numbers could represent side lengths of a right triangle?
Answer:
6m,8m,10m
Step-by-step explanation:
6m,8m,10m represent side lengths of a right triangle.
Proof :
for right angled triangle,
p^2 + b^2 = h ^ 2
6^2 + 8^2 = 10^2
36 + 64 = 100
100= 100{True}
proved
Answer:6m,8m,10m
Step-by-step explanation:
Garrett throws a dart at a circular dart board. the dart board has a radius of 16 inches and the bull's eye in the center of the dart board has a radius of 6 inches. what is the probability that a dart thrown at random within the dartboard will hit the bull's eye? round your answer to the nearest tenth, if necessary
Answer:14.1%
Step-by-step explanation:
What is the approximate solution to this equation?
7e^6x=42
Answer:
Rounding to nearest tenth, the answer is 0.3.
Step-by-step explanation:
[tex]\sf 7e^{6x}=42\\\frac{7e^{6x}}{7}=\frac{42}{7}\\e^{6x}=6\\[/tex]
[tex]\sf 6x = \ln(6)\\\\isolate~"x"~and~re-arrange\\\\x=\frac{\ln(6)}{6}[/tex]
≈ [tex]0.3[/tex]
If x=-3 and 2x+5y=-1 what is the value of y?
Answer:
y=1
Step-by-step explanation:
Start by plugging in -3 for x in the equation 2x+5y=-1 then solve for y.
2(-3)+5y=-1
-6+5y=-1 (add 6 to both sides)
5y=5 (divide both sides by 5)
y=1