Given the geometric sequence 100, 50, 25, ..., find the 7th term.
One number is 6 more than another. the difference between their squares is 192. what are the numbers?
The simplest form of square root of eighty can be written as a times square root of b, where a = and b = .
The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
Evaluate the expression. If necessary, round to the nearest hundredth.
log 1,000
3
103
1/3
Ben brought two pizzas to a party. He says that sinceramente 1/4 of each pizza is left,the sale a Mountain of each pizza is left. What is his error?
Final answer:
Ben incorrectly assumed that ¼ of two pizzas combined would still be ¼; however, the correct sum is ¼ + ¼ which equals ½ of a pizza. To add fractions, only the numerators are added when denominators match. Mastery of fractions is critical in both academics and day-to-day life.
Explanation:
Ben's error lies in the misunderstanding of fractions and how they add up. If Ben has two pizzas and each has ¼ left, combining the two portions does not result in having ½ of a pizza, but instead, he would have ¼ + ¼ which equals ½. This is because when adding fractions, you only add the numerators (the top numbers) if the denominators (the bottom numbers) are the same. Therefore, ¼ of one pizza plus ¼ of another pizza would equal ½ of a pizza. It's important to understand that fractions represent parts of a whole and that these parts must be added correctly to find the total amount.
Being comfortable with fractions is important not only for academic success but also for everyday life, such as understanding discounts, following recipes, or splitting bills. Utilizing real-life examples like these can help strengthen one's intuitive sense of fractions and make mathematical concepts more relatable.
What is the x-intercepts of the graph of y = 12x-5x-2
Please help me !! Thank you!!
A human gene carries a certain disease from the mother to the child with a probability rate of 70%. suppose a female carrier of the gene has three children. also assume that the infections of the three children are independent of one another. find the probability that at least one child gets the disease from their mother.
The probability that at least one of the three children gets the disease from their mother is 97.3%.
To find the probability that at least one child gets the disease from their mother when a female carrier of the gene has three children, we can follow these steps:
1. Define the probabilities:
- Probability that a child gets the disease from their mother (given): [tex]\( P(D) = 0.70 \)[/tex].
- Probability that a child does not get the disease from their mother: [tex]\( P(D^c) = 1 - P(D) = 0.30 \)[/tex].
2. Identify the total number of children:
- Number of children: [tex]\( n = 3 \)[/tex].
3. Calculate the probability that none of the children get the disease:
- For all three children to not get the disease, the probability is [tex]\( (P(D^c))^n = (0.30)^3 \)[/tex].
4. Find the probability that at least one child gets the disease:
- The probability that at least one child gets the disease is the complement of the probability that none of the children get the disease.
- Thus, [tex]\( P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) \)[/tex].
Let's do the calculations step by step.
Step-by-Step Calculations:
1. Calculate the probability that none of the children get the disease:
[tex]\[ P(\text{none of the children get the disease}) = (P(D^c))^3 = (0.30)^3 \][/tex]
2. Perform the exponentiation:
[tex]\[ (0.30)^3 = 0.30 \times 0.30 \times 0.30 = 0.027 \][/tex]
3. Calculate the probability that at least one child gets the disease:
[tex]\[ P(\text{at least one child gets the disease}) = 1 - P(\text{none of the children get the disease}) = 1 - 0.027 = 0.973 \][/tex]
Conclusion:
The probability that at least one child gets the disease from their mother is [tex]\( 0.973 \)[/tex], or 97.3%.
What should I do ???
Which unit should be studied to review symbols from set theory? Unit 1 Unit 3 Unit 5 Unit 7
A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. Let w = quarts of water left in the tub and t = time in minutes.
Is there a viable solution when time is 30 minutes? Answer: No, the tub will be empty by then.
A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute.
Let w be the quarts of water left in the tub.
Let t be the time in minutes.
So, the equation to model this situation is :
Modelling equation: [tex]w=50-2.5t[/tex]
This equation is viable only up to when t is 20 minutes. That will give w = 0. More than 20 minutes is not possible.
an internet company charges a one time setup fee of 44.99 and a monthly fee of 29.99 for internet service the company is offering a 25 percent discount on the monthly fee for the first year
HOW ARE RESTRICTIONS AND DISCONTINUITIES CREATED IN RATIONAL EXPRESSIONS? HOW CAN THEY BE ACCOUNTED FOR GRAPHICALLY?
In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator zero, as division by zero is undefined. Graphically, these are represented as vertical asymptotes or holes. They can be accounted for by noting the x-values where the denominator equals zero.
Explanation:In mathematics, discontinuities and restrictions in rational expressions are caused by values that make the denominator of the expression equal to zero, as division by zero is undefined. A rational expression is a ratio of two polynomials, typically written in the form P(x)/Q(x), where P(x) and Q(x) are polynomial expressions and x is a variable.
For example, in the rational expression (x+2)/(x-3), x-3 is the denominator. The restriction is determined by setting the denominator equal to zero. If x-3 equals zero, then the value of x that makes this true is 3. Therefore, x cannot be 3 as this would make the denominator zero, creating a discontinuity in the rational expression.
Graphically, discontinuities in rational expressions are represented as vertical asymptotes or holes. A vertical asymptote occurs when the denominator of the fraction is zero but the numerator is not. A hole occurs when both the numerator and the denominator are zero at the same point. These can be accounted for by noting the x-values where the denominator equals zero.
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There's a 40% chance of rain on Tuesday and a 50% chance of rain Friday. What percent will it rain both Tuesday and Friday?
p.s. this is a probability question I think
What is the circumference of the circle in terms of pi? The radius is 2.2 and I got 13.82 but the choices are 1.1, 1.21, 2.2 and 4.4 im so confused so could someone please explain what i did wrong?
Pepe is putting a fence in his backyard to enclose the garden in form of a triangle. The garden already has sides enclosed with 8 feet and 5 feet of fence, respectively. What can you say about the length of the third side?
Answer:
Step-by-step explanation:
Pepe is putting a fence in his backyard to enclose the garden in the form of a triangle.
In the garden already has sides enclosed with 8 feet and 5 feet.
We know a triangle is possible when sum of length of two sides > third side
so third side < 8 + 5
or third side should be less than 13.
simplify this expression. (√2 + √3)(√5 - √7)
The simplified expression is √10 - √14 + √15 - √21.
To simplify the expression (√2 + √3)(√5 - √7), we can use the distributive property of multiplication.
Expanding the expression, we get:
(√2 + √3)(√5 - √7) = √2 x √5 + √2 x (-√7) + √3 x √5 + √3 x (-√7)
Now, simplifying each term with FOIL method we have:
√2 * √5 = √(2 x 5) = √10
√2 * (-√7) = -√(2 x 7) = -√14
√3 * √5 = √(3 x 5) = √15
√3 * (-√7) = -√(3 x 7) = -√21
Combining the simplified terms, we get:
√10 - √14 + √15 - √21
Therefore, the simplified expression is √10 - √14 + √15 - √21.
In this process, we applied the distributive property to expand the expression and then simplified each term by multiplying the square roots together. Finally, we combined the like terms to obtain the simplified expression.
For more such answers on the FOIL method
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Answer:
√10 + √15 - √14 - √21
Step-by-step explanation:
(√2 + √3)(√5 - √7)
= √2(√5 - √7) + √3(√5 - √7)
= √10 - √14 + √15 - √21
= √10 + √15 - √14 - √21
Suppose we set θ0=−2,θ1=0.5 in the linear regression hypothesis from q1. what is hθ(6)?
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For the function f(x)= square root (x-5), find f^-1. What is the range of f^-1? Any explanation and answer is appreciated!!
Final Answer:
The inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex] or [5, ∞].
Explanation:
To find the inverse function, [tex]\( f^{-1} \)[/tex], for the function [tex]\( f(x) = \sqrt{x-5} \)[/tex], we'll need to follow these steps:
1. Write the function as an equation: [tex]\( y = \sqrt{x-5} \)[/tex].
2. To find the inverse, we exchange the roles of x and y. The equation now reads [tex]\( x = \sqrt{y-5} \)[/tex].
3. Our next task is to solve this equation for y. To do so, we need to eliminate the square root by squaring both sides of the equation:
[tex]\[ x^2 = (\sqrt{y-5})^2 \\\\\[ x^2 = y - 5 \][/tex]
Now, we add 5 to both sides in order to isolate y:
[tex]\[ y = x^2 + 5 \][/tex]
This is our inverse function: [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex].
Regarding the range of [tex]\( f^{-1} \)[/tex], we need to consider the domain of the original function f(x). The original function [tex]\( f(x) = \sqrt{x-5} \)[/tex] is only defined for [tex]\( x \geq 5 \)[/tex], because you cannot take the square root of a negative number in real numbers.
Since the domain of f(x) becomes the range of [tex]\( f^{-1}(x) \)[/tex], the range of the inverse function must be [tex]\( y \geq 5 \)[/tex], because the smallest value of x is 5, which when inputted into the inverse gives us [tex]\( 5^2 + 5 = 25 + 5 = 30 \)[/tex], and it only grows larger for larger values of x.
So the inverse function is [tex]\( f^{-1}(x) = x^2 + 5 \)[/tex] and the range of [tex]\( f^{-1} \)[/tex] is [tex]\( y \geq 5 \)[/tex].
find the nonpermissible replacement for y in this expression Y+7/Y-3
Final answer:
The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.
Explanation:
The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.
Steps to find the nonpermissible value:
Identify the denominator of the expression, which is (Y-3).
Set the denominator equal to zero: Y - 3 = 0.
Solve for y: Y = 3.
Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.
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At an amusement park, the probability that a child eats a hot dog and drinks a soda pop is 0.38. The probability that a child eats a hot dog is 0.61, and the probability that a child drinks soda pop is 0.89. What is the probability (rounded to the nearest hundredth) that a child drinks soda pop given that the child has already eaten a hot dog? Hint: cap p left parenthesis cap a vertical line cap b right parenthesis equals start fraction cap p left parenthesis cap a intersection cap b right parenthesis over cap p left parenthesis cap b right parenthesis end fraction
A| 0.34
B| 0.43
C| 0.62
D| 0.69
Which ratios form a proportion?
3/15, 12/55
8/24, 12/35
5/18, 25/90
4/11, 16/25
What ratio forms a proportion with 9/15?
6/10
16/21
36/50
45/70
Answer: 1. C) 5/18, 25/90
2. A) 6/10
Step-by-step explanation: 1) We need to find the ratios those makes a proportion:
Let us check given options one by one.
3/15, 12/55
Converting them into simplest fractions.
3÷3/15÷3 = 1/5
12/55 can't be reduce more.
1/5 ≠ 12/55
So, 3/15, 12/55 don't form a proportion.
8/24, 12/35
Converting them into simplest fractions.
8÷8/24÷8 = 1/3
12/35 can't be reduce more.
8/24 ≠ 12/35
So, 8/24, 12/35 don't form a proportion.
So, 5/18, 25/90 form a proportion.
4/11, 16/25
Converting them into simplest fractions.
4/11 and 16/25 both can't be reduce more.
4/11≠16/25
So, 4/11, 16/25 don't form a proportion.
___________________________________________________
Let us reduce 9/15 into simplest fraction.
9÷3/15÷3 = 3/5Now, let us convert each and every option in simplest fractions.
6÷2/10÷2 = 3/516÷1/21÷1 = 16/21
36÷2/50÷2 = 18/25
45÷5/70÷5 = 9/14
We can see 6/10 gives lowest fraction 3/5 as 9/15 gives.
Therefore, 6/10 form a proportion with 9/15.
Sharon and Jacob started at the same place. Jacob walked 3 m north and then 4 m west. Sharon walked 5 m south and 12 m east. How far apart are Jacob and Sharon now?
Consider the coordinate plane:
1. The origin is the point where Sharon and Jacob started - (0,0).
2. North - positive y-direction, south - negetive y-direction.
3. East - positive x-direction, west - negative x-direction.
Then,
if Jacob walked 3 m north and then 4 m west, the point where he is now has coordinates (-4,3);if Sharon walked 5 m south and 12 m east, the point where she is now has coordinates (12,-5).The distance between two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be calculated using formula
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.[/tex]
Therefore, the distance between Jacob and Sharon is
[tex]D=\sqrt{(12-(-4))^2+(-5-3)^2}=\sqrt{16^2+8^2}=\sqrt{256+64}=\sqrt{320}=8\sqrt{5}\approx 11.18\ m.[/tex]
Find the constant rate of change for each linear function and interpret their meaning.
A cone with volume 5000 m³ is dilated by a scale factor of 15. What is the volume of the resulting cone? Enter your answer in the box. m³
Answer:
[tex]40\ m^{3}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> scale factor
x-----> the volume of the dilated cone
y-----> the volume of the original cone
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=1/5[/tex]
[tex]y=5,000\ m^{3}[/tex]
substitute and solve for x
[tex](1/5)^{3}=\frac{x}{5,000}[/tex]
[tex](1/125)=\frac{x}{5,000}[/tex]
[tex]x=5,000/125=40\ m^{3}[/tex]
Write an equation that is perpendicular to y = -7x + 2 and passes through (7 , 5)
Fuel prices have increased by 9% this year. The smiths family’s fuel bill for this year is now £1956. How much was the bill likely to have been last year
is (0,0) a solution to this system? y ≥ x^2 + x - 4, y> x^2 + 2x + 1
Final Answer:
The point (0,0) does not satisfy the inequality [tex]y ≥ x^2[/tex] + x - 4, as 0 is not greater than or equal to -4. Additionally, it does not satisfy [tex]y > x^2 + 2x + 1[/tex], as 0 is not greater than 1. Therefore, (0,0) does not meet the conditions of the system of inequalities.
Step-by-step explanation:
The point (0,0) is not a solution to the given system of inequalities. First, considering the inequality [tex]y ≥ x^2 + x - 4[/tex], when substituting x=0 and y=0 into the equation, we find that 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the conditions of the first inequality. Moving on to the second inequality, [tex]y > x^2 + 2x + 1[/tex], substituting x=0 and y=0 results in 0 not being greater than 1.
Consequently, (0,0) fails to meet the requirements of the second inequality as well. In summary, the point (0,0) does not simultaneously satisfy both inequalities, rendering it unsuitable as a solution to the system.
Analyzing solutions to systems of inequalities involves evaluating each inequality independently to ensure the chosen point satisfies all conditions. In this instance, the failure of (0,0) to satisfy either inequality demonstrates that it does not conform to the system's criteria. When dealing with systems of inequalities, it is essential to carefully assess each component to accurately determine the solution set.
No, (0,0) is not a solution to the given system.
Explanation:The system consists of two inequalities: y ≥ x^2 + x - 4 and y > x^2 + 2x + 1. To check whether (0,0) is a solution, substitute x = 0 and y = 0 into both inequalities. For the first inequality, x^2 + x - 4 becomes -4, and 0 is not greater than or equal to -4. Therefore, (0,0) does not satisfy the first inequality. Moving on to the second inequality, x^2 + 2x + 1 becomes 1, and 0 is not greater than 1. Hence, (0,0) fails to satisfy the second inequality as well. As a result, (0,0) is not a solution to the system of inequalities.
In summary, by substituting the coordinates of (0,0) into both inequalities, we find that the point does not meet the conditions set by either inequality. Therefore, (0,0) is not a solution to the system. This conclusion is based on the specific values obtained through substitution, demonstrating that the coordinates do not satisfy the given inequalities.
If a company is considering the purchase of a parcel of land that was acquired by the seller for $93,000 is offered for sale at $166,000, is assessed for tax purposes at $103,000, is recognized by the purchaser as easily being worth $156,000, and is purchased for $153,000, the land should be recorded in the purchaser's books at:
Answer:
The land should be recorded in the purchaser's books at : $153,000.
Step-by-step explanation:
Since the parcel of land is purchased by the company for $153,000, hence the land should be recorded in the purchaser's books at : $153,000.