Answer: A) 1/49
Step-by-step explanation:
Since the spinner has seven equal sections numbered 1 through 7, the theoretical probability of landing on any particular number on a single spin is 1/7.
To find the theoretical probability that the spinner lands on 2 and then an odd number, we can multiply the probability of landing on 2 on the first spin by the probability of landing on an odd number on the second spin.
The probability of landing on 2 on the first spin is 1/7, and the probability of landing on an odd number on the second spin is 3/7 (there are three odd numbers among the remaining six sections).
Therefore, the theoretical probability of the spinner landing on 2 and then an odd number is:
(1/7) x (3/7) = 3/49
So the answer is A) 1/49.
PLS HELP I WILL MARK BRAINILEST
Answer:
Let's assume the original price of the stock was x.
When the company announced it overestimated demand, the stock price fell by 40%.
So, the new price of the stock after the first decline was:
x - 0.4x = 0.6x
A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.
So, the new price of the stock after the second decline was:
0.6x - 0.6(0.6x) = 0.24x
Given that the current stock price is $2.40, we can set up the equation:
0.24x = 2.40
Solving for x, we get:
x = 10
Therefore, the stock was originally selling for $10.
Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
HELP! I WILL AMKE YOU BRAINLIEST BC THIS IS DUE TODAY!!!
Answer: 27.3
Step-by-step explanation:
I took the outcomes of the Aces from the trial and found the average and the answer I got was 27.3%
Hope this helps.
The windows to a Tudor-style home create many types of quadrilaterals. Use the picture of the window below to answer the following questions.
Please help me I will give literally anything
a. Determine which type of quadrilaterals you see. Name these quadrilaterals using the labeled vertices.
b. What properties of quadrilaterals would you have to know to identify the parallelograms in the picture? Be specific as to each type of parallelogram by using the properties between sides, angles, or diagonals for each.
Answer:
I'd be happy to help!
a. From the picture of the window, we can identify the following quadrilaterals:
Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)
Parallelogram: EFGH (opposite sides are parallel and congruent)
Trapezoid: BCGH (at least one pair of opposite sides are parallel)
b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:
Opposite sides are parallel and congruent
Opposite angles are congruent
Diagonals bisect each other
Using these properties, we can identify the following parallelograms in the picture:
Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.
Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.
Step-by-step explanation:
The roof on a house requires that every 2 yards gets covered by 3 shingles. You currently have 60 boxes that contain 120 shingles each. The roof of the house is estimated at 4500 yards that must be covered. Which sentence best describes the amount of shingles needed?
To cover the house roof, as we only need 6,750 shingles and we have 7,200 shingles available.
What are arithmetic operations ?
Arithmetic operations are basic mathematical operations used to perform calculations involving numbers. The four basic arithmetic operations are:
Addition: This operation involves combining two or more numbers to get a total or sum. The symbol used for addition is "+".Subtraction: This operation involves finding the difference between two numbers. The symbol used for subtraction is "-".Multiplication: This operation involves finding the product of two or more numbers. The symbol used for multiplication is "×" or "*".Division: This operation involves dividing a number into equal parts or finding how many times one number fits into another. The symbol used for division is "÷" or "/".According to the question:
To determine the amount of shingles needed to cover the roof of the house, we can use the fact that every 2 yards requires 3 shingles. Therefore, for 4500 yards, we need to divide by 2 and then multiply by 3 to get the total number of shingles needed.
(4500 yards) / (2 yards/2) * (3 shingles/2 yards) = 6,750 shingles
Since we have 60 boxes that contain 120 shingles each, we can calculate the total number of shingles we have:
60 boxes * 120 shingles per box = 7,200 shingles
Therefore, we have more than enough shingles to cover the roof, as we only need 6,750 shingles and we have 7,200 shingles available.
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An 8 foot long ladder is leaning against a wall. The top of the ladder is sliding down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall.
"The rate at which the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall is calculated to be 3.464 ft/s."
At a pace of 2 feet per second, the lower end of the ladder is being pulled away from the wall.
At a specific moment, when the lower end of the ladder is 4 feet from the wall, we should determine the rate at which the bottom of the ladder is lowering.
From the point t, the bottom of the ladder is x m, the top of the ladder is y m from the wall.
x² + y² = 64
Differentiating the given relationship with regard to t,
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
We need to find out dx/dt at x = 4.
dy/dt = -2
At x = 4, we have,
x² + y² = 64
16 + y² = 64
y² = 48
y = 4√3
Put in the known values to find out dx/dt,
x dx/dt + y dy/dt = 0
4 dx/dt + 4√3 (-2) = 0
4 dx/dt = 8√3
dx/dt = 2√3 = 3.464
Thus, the bottom of the ladder is calculated to be moving at the rate 3.464 ft/s.
The figure can be drawn as shown in the attachment.
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2. The directions for sewing a scarf says that you must purchase 1.75 yards of fleece
fabric. The cost per yard is $10.30. How much will you need to spend on fleece fabric?
Answer:
$18.03
Step-by-step explanation:
10.30 x 1.7 = 18.025
round answer to 18.3
Answer: $18.03
Step-by-step explanation:
1.75 x 10.3 = 18.025
18.025 ≈ 18.03
for each polynomial in factored form show the leading term, the zeros on the x-axis, and the general shape of the polynomial
For the given polynomials in factored form;
(a) the leading term is x³, the zeroes are -2,3 and 5 , the graph will be a cubic function passing through x-axis at -2, 3 and 5.
(b) the leading term is 2x², the zeros are -1, 4 the graph will be a quadratic function passing through x-axis at -1 and 4.
Part(a) : The polynomial in factored form is : f(x) = (x + 2)(x - 3)(x - 5)
The Leading Term is : x³; The Zeros are : -2, 3, 5.
The General Shape: The graph of the polynomial will be a cubic function that passes through the x-axis at -2, 3, and 5.
The function will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.
Part(b) : The Polynomial in factored form is : f(x) = 2(x + 1)(x - 4)
The Leading Term is : 2x²; The Zeros are : -1, 4.
The General Shape: The graph of the polynomial will be a quadratic function that passes through the x-axis at -1 and 4. The function will open upwards since the leading coefficient is positive.
The function will approach negative infinity as x approaches negative infinity and positive infinity as x approaches positive infinity.
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The given question is incomplete, the complete question is
For each polynomial in factored form show the leading term, the zeros on the x-axis, and the general shape of the polynomial.
(a) f(x) = (x + 2)(x - 3)(x - 5)
(b) f(x) = 2(x + 1)(x - 4).
10 points! HELP ASAP PLEASE HELP ME FIND THE AREA and the perimeter
Answer:
307ft^2
Step-by-step explanation:
To explain this, you are looking for the area of half a circle + the area of a triangle.
To first find the area of half a circle, we need the equation Area = pir^2/2
Plug-in radius, which is 10ft
pi(10)^2/2
= 157ft^2
Next, we find the area of the triangle. The equation to find the area of a triangle is A=1/2(b)(h)
B=base
h=height
To find the base, we simple make the base equal to the diameter of the circle, which is the radius multiplied by 2
So base = 10*2 = 20
The height is given so
height=15
Plug in base and height = 20*15/2
= 150ft^2
Then you want to add both areas found together
157ft^2+150ft^2
= 307ft^2
Expand and simplify completely
[tex]x(x+(1+x)+2x)-3(x^2-x+2)[/tex]
Answer:
x² + 4x - 6
Step-by-step explanation:
x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left
= x(x + 1 + x + 2x) - 3(x² - x + 2)
= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis
= 4x² + x - 3x² + 3x- 6 ← collect like terms
= x² + 4x - 6
find the t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (d f).
The t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df) is 1.753050356.
We have to determine the t-value.
The area in the right tail is 0.10 with 32 degrees of freedom(df).
The t-test is a test that is used as an alternative to the z-test in statistics. If the data are normally distributed but the sample size is small and the population standard deviation is unknown, the t-test is utilized.
A value that appears on the t distribution is the critical t value. The area under the curve and the degrees of freedom can be used to determine the t statistic value.
Using Excel Formula,
The t-value = (=TINV(0.1,15))
The t-value = 1.753050356
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CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy?
Answer:
9 CDs
Step-by-step explanation:
r u d0mb? 45 divided by 5 = 5 10 15 20 25 30 35 40 45
count the numbers
BOOM ANSWER
NEXT TIME PAY ATTENTION IN 2ND GRADELet X1, X2, ..., Xn denote n independent and identically distributed Bernoulli random vari- ables s.t. P(X; = 1) = p and P(Xi = 0) = 1 – p. for each i = 1, 2, ..., n. Show that __, Xi is sufficient for p by using the factorization criterion given in Theorem 9.4. THEOREM 9.4 Let U be a statistic based on the random sample Yı, Y2, ..., Yn. Then U is a sufficient statistic for the estimation of a parameter 0 if and only if the likelihood L(0) = L(y1, y2, ..., yn 10) can be factored into two nonnegative functions, L(y1, y2, ..., yn (0) = g(u,0) x h(yı, y2, ..., yn) where g(u,0) is a function only of u and 0 and h(y1, y2, ..., yn) is not a function of o.
The likelihood function can be factored using Theorem 9.4 as L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn), where g(Σⁿᵢ=1Xᵢ, p) = p^Σⁿᵢ=1Xᵢ (1-p)^(n-Σⁿᵢ=1Xᵢ) and h(X₁, X₂, ..., Xn) = 1. This satisfies the factorization criterion, and thus, Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
To show that Σⁿᵢ=1Xᵢ is sufficient for p, we need to show that the likelihood function can be factored using Theorem 9.4 as:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
where g(Σⁿᵢ=1Xᵢ, p) is a function only of Σⁿᵢ=1Xᵢ and p, and h(X₁, X₂, ..., Xn) is not a function of p.
First, we can write the joint probability mass function of X₁, X₂, ..., Xn as:
P(X₁ = x₁, X₂ = x₂, ..., Xn = x_n) = p^Σⁿᵢ=1xᵢ (1-p)^Σⁿᵢ=1(1-xᵢ)
Taking the product of these probabilities for all i, we get:
L(p) = L(X₁, X₂, ..., Xn | p) = Πⁿᵢ=1P(Xᵢ = xᵢ) = p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)
Using the factorization criterion given in Theorem 9.4, we need to find functions g(u, p) and h(X₁, X₂, ..., Xn) such that:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
Let's take g(u, p) = pᵘ(1-p)⁽ⁿ⁻ᵘ⁾, which only depends on u and p. Then:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
= p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ) * h(X₁, X₂, ..., Xn)
We can see that the term Σⁿᵢ=1Xᵢ appears in the exponent of p, and Σⁿᵢ=1(1-Xᵢ) appears in the exponent of (1-p). Therefore, we can write:
L(p) = L(X₁, X₂, ..., Xn | p) = [p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)] * [1]
where the second factor is a constant function of p. This satisfies the factorization criterion, with g(u, p) = pᵘ(1-p⁽ⁿ⁻ᵘ⁾ and h(X₁, X₂, ..., Xn) = 1.
Therefore, we have shown that Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
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Complete question is in the image attached below
Type the correct answer in each box. Assume π = 3.14. Round your answer(s) to the nearest tenth. 90° 30° In this circle, the area of sector COD is 50.24 square units. The radius of the circle is units, and m AB is units.
Therefore, the length of segment AB is approximately 7.4 units.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.
Here,
To find the radius of the circle, we can use the formula for the area of a sector:
Area of sector = (θ/360) x π x r²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.
We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:
50.24 = (90/360) x 3.14 x r²
50.24 = 0.25 x 3.14 x r²
r² = 50.24 / (0.25 x 3.14)
r² = 201.28
r = √201.28
r ≈ 14.2
Therefore, the radius of the circle is approximately 14.2 units.
Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:
AB = 2 x r x sin(θ/2)
where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.
We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:
AB = 2 x 14.2 x sin(30/2)
AB = 2 x 14.2 x sin(15)
AB ≈ 7.4
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Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Cookies are on sale! Today each cookie costs
$
0.75
$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you buy
7
77 of them it will only cost you
$
2.80
$2.80dollar sign, 2, point, 80!
Write an equation to determine the normal price of each cookie
(c)
(c)left parenthesis, c, right parenthesis.
The correct answer is:
The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].
Explanation:
c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].
We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:
[tex]7(c-0.75) = 2.80[/tex]
To solve, first use the distributive property:
[tex]7 \times c-7\times0.75 = 2.80[/tex]
[tex]7c-5.25 = 2.80[/tex]
Add 5.25 to each side:
[tex]7c-5.25+5.25 = 2.80+5.25[/tex]
[tex]7c = 8.05[/tex]
Divide each side by 7:
[tex]7c\div7 = 8.05\div7[/tex]
[tex]c = \$1.15[/tex].
Dish A had cells with a radius of 5.1 x10-10 cm. Dish B had cells that had a radius of 4.1 x 10-8 cm. What is the sum of the radii of the two types of cells, using scientific notation?
Answer:
Step-by-step explanation:
To find the sum of the radii of the two types of cells in scientific notation, we need to add the two radii together. However, the radii are given in different orders of magnitude (exponents), so we need to convert one of the radii to match the order of magnitude of the other radius.
The radius of dish A cells is 5.1 x 10^-10 cm.
The radius of dish B cells is 4.1 x 10^-8 cm.
We can convert the radius of dish A cells to match the order of magnitude of dish B cells by multiplying it by 100 (10^2), which gives us:
5.1 x 10^-10 cm x 10^2 = 5.1 x 10^-8 cm
Now that both radii have the same order of magnitude (10^-8), we can add them together to get the total sum of the radii:
5.1 x 10^-8 cm + 4.1 x 10^-8 cm = 9.2 x 10^-8 cm
Therefore, the sum of the radii of the two types of cells, in scientific notation, is 9.2 x 10^-8 cm.
Answer:9.2 x 10^-8 cm.
Step-by-step explanation:
4) 6 out of the 80 dogs in a shelter were adopted yesterday. Express adopted rate as a percent.
Answer:
Step-by-step explanation:
To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.
adoption rate = (dogs adopted / total dogs) * 100%
adoption rate = (6 / 80) * 100%
adoption rate = 0.075 * 100%
adoption rate = 7.5%
Therefore, the adoption rate as a percent is 7.5%.
the temperature on monday was ₋7∝.
the temperature on tuesday was 5∝ lower than on monday.
the temperature on wednesday was 8∝ higher than on tuesday.
find the temperature on wednesday.
Answer:
пошел в
Step-by-step explanation:
The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5) calculate the corresponding z-scores for the following 6 American’s weekly beer intake.
The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
1. 5 beers per week: z-score = -1
2. 8 beers per week: z-score = +1
3. 10 beers per week: z-score = +2
4. 4 beers per week: z-score = -2
5. 6 beers per week: z-score = -0.5
6. 12 beers per week: z-score = +3
To calculate a z-score, we need to know the mean (μ) and standard deviation (σ) of the population. In the given problem, the mean is 7 beers per week, and the standard deviation is 1.5.
A z-score is the number of standard deviations away from the mean. Therefore, to calculate the z-scores, we subtract the mean from the given data point and divide by the standard deviation.
For example, for 5 beers per week, the z-score is (-1). This is calculated by subtracting the mean (7) from the data point (5) and dividing by the standard deviation (1.5). Therefore, (5-7)/1.5 = -1.
Similarly, the z-score for 8 beers per week is (+1). This is calculated by (8-7)/1.5 = +1. The z-score for 10 beers per week is (+2). This is calculated by (10-7)/1.5 = +2. The z-score for 4 beers per week is (-2). This is calculated by (4-7)/1.5 = -2. The z-score for 6 beers per week is (-0.5). This is calculated by (6-7)/1.5 = -0.5.The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
the complete question is :
The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5), calculate the corresponding z-scores for the following 6 Americans’ weekly beer intake:
a) Bob drinks 9 beers per week
b) Sarah drinks 6 beers per week
c) John drinks 4 beers per week
d) Emily drinks 8 beers per week
e) Michael drinks 10 beers per week
f) Rachel drinks 5 beers per week
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A charge Q1 = –1.6 x 10–6 coulomb is fixed on the x–axis at +4.0 meters, and a charge Q2 = + 9 x 10–6 coulomb is fixed on the y–axis at +3.0 meters, as shown on the diagram above. a. i. Calculate the magnitude of the electric field E1 at the origin O due to charge Q1. ii. Calculate the magnitude of the electric field E2 at the origin O due to charge Q2. iii. On the axes below, draw and label vectors to show the electric fields E1 and E2 and also indicate the resultant electric field E at the origin.
a. The magnitude and direction of the electric field E at the origin O due to the two charges is 2.29 × 10⁴ N/C.
b. The electric potential V at the origin is zero
a. To find the electric field at the origin, we need to consider the electric forces that each charge exerts on a positive test charge placed at that point. The magnitude of the electric field E at the origin is given by the formula:
E = k * |Q₁| / r₁² + k * |Q₂| / r₂²,
where k is Coulomb's constant, |Q₁| and |Q₂| are the magnitudes of the charges, and r₁ and r₂ are the distances from each charge to the origin.
In this case, Q₁ = − 1.6 × 10⁻⁶ C and Q₂ = + 9 × 10⁻⁶ C, so the magnitude of the electric field at the origin is:
E = k * |Q₁| / r₁² + k * |Q₂| / r₂²
= 9 × 10⁹ N·m²/C² * |− 1.6 × 10⁻⁶ C| / (4 m)² + 9 × 10⁹ N·m²/C² * |+ 9 × 10⁻⁶ C| / (3 m)²
= 2.29 × 10⁴ N/C.
b. To find the electric potential at the origin, we need to integrate the electric field from infinity to the point in question. The electric potential V at the origin is given by the formula:
V = − ∫ E · dr
where the integral is taken along any path from infinity to the origin. Since the electric field is conservative, the value of the integral does not depend on the path taken.
Therefore, we can choose a path that goes straight from infinity to the origin, and the integral simplifies to:
V = − ∫ E · dr = − E ∫ dr = − E x r,
where r is the distance from the origin to the point where the test charge is located. Since we are interested in the potential at the origin, we set r = 0 and obtain:
V = 0.
Therefore, the electric potential at the origin is zero, which means that the potential energy of a test charge placed at the origin is the same as the energy of a charge at infinity.
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Complete Question:
A charge Q₁ = − 1.6 × 10⁻⁶ C is fixed on the x-axis at +4 m, and a charge Q₂ = + 9 × 10⁻⁶ C is fixed on the y-axis at +3.0 m.
a. Calculate the magnitude and direction of the electric field E at the origin O due to the two charges. Draw and clearly label this vector on a coordinate axis.
b. Calculate the electric potential V at the origin.
taking a whole number, how do you know if there is a number that you can multiply by itself to get it
If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.
Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.
However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.
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Find the equation of a parabola with a focus at (-4, 7) and a directrix of
y = 1,
Oy-7=(x+4)²
Oy-3=(x+4)²
Oy+4= (-4)²
Oy-4=(+4)²
According to the question,the equation of the parabola is y = (x + 4)² - 6.
What is equation?An equation is a statement that equates two expressions using mathematical symbols. It is a mathematical statement that two expressions are equal in value. Equations can involve numbers, variables, and constants. Equations are used to solve real-world problems such as determining the speed of a car from the distance traveled and time elapsed.
The equation of a parabola with a focus at (-4, 7) and a directrix of y = 1 is given by:
y = (x + 4)² + 4.
This equation is derived from the standard equation of a parabola:
y = (x - h)² + k,
where (h, k) is the coordinates of the focus.
In this case, the coordinates of the focus are (-4, 7), so the equation becomes:
y = (x + 4)² + 7.
The directrix of the parabola is a line, so its equation is given by:
y = 1.
Substituting this equation into the equation of the parabola, we get:
(x + 4)² + 7 = 1
(x + 4)² = -6
y = (x + 4)² - 6.
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The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
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The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.4, what is P(A or B)?
Round your answer to two decimal places.
i need help on these 2 !!!
The length of RS is 13 units and the length of the hypotenuse XY is approximately 16.4 units.
15) In ΔTSR
TR² = TS² + RS²
Substituting the given values, we get:
(5√10)² = 9² + RS²
250 = 81 + RS²
RS² = 169
Taking the square root of both sides, we get:
RS = 13 units
16)In ΔYZX
XY² = YZ² + XZ²
Substituting the given values, we get:
XY² = 10² + 13²
XY² = 169 + 100
XY² = 269
Taking the square root of both sides, we get:
XY = √269
XY=16.4 units
What is Pythagorean theorem?
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?
5/9=
1/14=
12/13=
2/13=
9/11=
9/17=
To round each fraction
Answer:
Step-by-step explanation:
1. Rounded to 0.56
2. Rounded
HELP ME ASAP!!! YOU WILL BE BRAILIEST!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
given the following limit lim(x;y)!(0;0) infinty y infinity y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).
To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.
We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).
To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have
lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.
However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have
lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.
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