(23)/4)-6×69(7+8)0-(5)2897)
​

Answer:

Step-by-step explanation:

\(f(x)=a(x-h)^2+k\)    vertex form of equation with vertex (h, k)

\(\left \big{f(x)=a(x-h)^2+k}\atop \big{f(x)=-(x-2)^2-3}\right\}\implies a=-1\,,\ h=2\,,\ k=-3\)

So vertex of  f(x) = - (x - 2)² - 3 is  (2, -3)

The x-intercepts of the given function are 2±√6.

What are the intercepts of a line?

A line crosses the x-axis at the x-intercept, and the y-intercept marks the spot where the line crosses the y-axis.

The given function is f(x) = x² -4x -2

To find the x-intercept we need to make f(x) = y = 0

So x² - 4x -2 = 0

x = [-b±√(b² -4ac)] /2a

where a =1

           b = -4

            c = -2

substituting the above values

x =[ -(-4) ±√ (-4)²-(4*1*-2) ] / 2 = [4±√(16 +8)]/2 = (4±2√6)/2 = 2±√6

Therefore the x-intercepts of the given function are 2±√6.

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Answer:

The answer is 9.9

Step-by-step explanation:

Answer:

99/10 or: 9 9/10 or: 9.9

Step-by-step explanation:

Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Hopes this help.

Ratio scale is an actual number of purchases in a certain time period, dollars spent, miles traveled, number of children in the household, or years of college education.

The ratio scale is the highest form of measurement and has all the properties of the nominal, ordinal, and interval scales.

It has an absolute zero point and measurements that can be mathematically operated on.

Therefore, it is easy to calculate ratios and compare magnitudes between different things with ratio scales. The zero point implies that nothing is available in the variable.

As a result, comparisons with ratios are more precise. The ratio scale is the most useful of the four scales of measurement because it allows for more precise and standardized measurement with mathematical operations.

Therefore, Ratio scale is an actual number of purchases in a certain time period, dollars spent, miles traveled, number of children in the household, or years of college education.

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The given sample size is 81 at 90% level of confidence. So the degree of freedom df = n - 1 = 80. To obtain the lower and upper critical values of χ², we use the Chi-square distribution table as shown below:χ²(0.05,80) = 101.879χ²(0.95,80) = 61.656

Where χ²(0.05,80) and χ² (0.95,80) are the lower and upper critical values of χ² at 0.05 (5%) and 0.95 (95%) levels of significance, respectively.

The formula to calculate the confidence interval for standard deviation of a population is given by:

\(\[\sqrt{\frac{(n-1)s^{2}}{\chi _{2}^{2}\left( \frac{\alpha }{2},n-1 \right)}}\)

\(<\sigma <\sqrt{\frac{(n-1)s^{2}}\)

\({\chi _{2}^{2}\left( 1-\frac{\alpha }{2},n-1 \right)}}\]\)

Where n = 81, s = 11.71, χ²(0.05,80) = 101.879 and χ²(0.95,80) = 61.656.Substitute the given values in the formula,\(\[\sqrt{\frac{(81-1)(11.71)^{2}}{101.879}}<\sigma <\sqrt{\frac{(81-1)(11.71)^{2}}{61.656}}\] \[10.441<\sigma <12.853\]\). Hence, the 90% confidence interval for σ, the true standard deviation of resting heart rates for Rio Hondo students, is (10.441, 12.853).

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Answer:

1232 penny

Step-by-step explanation:

Given the value of a bank account, B, after x years is represented by the equation B = 1000(1+.014)^x.

To determine the account worth after 15 years, we will substitute x = 15 into the expression as shown;

B = 1000(1+.014)^x.

B = 1000(1+.014)^15

B = 1000(1.014)^15

B = 1000(1.2319)

B = 1231.9penny

Hence the value after 15years is 1232 penny (to the nearest penny)

Answer:24%

Step-by-step explanation:

When you multiply a fraction by 100 you will get the percent

12/50 x 100=24

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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how many students owned either a car or an ipod (but not both): =100−90=10

What is union of sets?

Union of two given sets is the littlest set which contains every one of the components of both the sets.

What is intersection of sets?

Intersection of two given sets is the biggest set which contains every one of the components that are normal to both the sets

What is the recipe for union of two sets?

The union of two sets is given by

n(A∪B) = n(A) + n(B) - n(A∩B)

Where,

An and B are the two sets.

∪ is the union

∩ is the intersection.

n(AUB)=n(A)+n(B)−n(A∩B)

     =80+60−50

=90

number of students owning a car or an ipod=90

number of students neither car nor stereo =100−90=10

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Answer:

points at (0,-1) and (1,4) will have a slope of 1/4 and a negative y-intercept

Step-by-Step Explanation:

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

Step-by-step explanation:

There's no diagram and no question, but I assume it shows a right triangle.

distance = √(14²+13²) = √365 ≅ 19.1 miles

Answer:

Please see the picture below.

Step-by-step explanation:

To calculate the slope between 2 points we use the following equation:

Replacing the points:

In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.

For the perpendicular case, the slope is equal to:

For the perpendicular case, the slope is zero and would equal one parallel to the X axis.

Answer:

Step-by-step explanation:

The question is asking us to find the slope.

First, we will find the slope of the line that passes through (4,8) and (4,6).

We'll use the slope formula:

\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data :

\(\bf{m=\dfrac{6-8}{4-4}}\)

\(\bf{m=\dfrac{-2}{0}}\)

\(\bf{m=not\:de fined}\)

If a line's slope is not defined, then it's a vertical line:

                                       \(\rule{1}{350}\)

------

Now, what is the slope of a line that's parallel to the one above? Well, since parallel lines have equal slopes, that one will have an undefined slope too.

As for perpendicular lines, they have slopes that are negative reciprocals of each other. We got that the slope is -2/0. The negative reciprocal of that is 0/2, which simplifies to 0.

Alternatively, you could look at it this way: a horizontal line (a line with zero slope) is perpendicular to a vertical line. So the slope of that line is m = 0.

\(\rule{350}{1}\)

Answer:

234

Hope this helps! :)

Answer:

n = -6

Step-by-step explanation:

10[6(n+1)+5(n-1)]=13[7(5+n)-(25-3)]

You will collect like terms

10(6n+6+5n-5)=13(35+7n-25+3)

it will give you this

10(11n+1)=13(10+10n)

Then you remove the parenthesis

110n+10 = 130 +130n

Move the terms

110n -130n = 130-10

collect like terms

-20n=120

divide both sides

n=-6

answer: E

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .

(b) The distance between points (2,-5) and (-7,-5) is 9 units .

(c) The midpoint of the line segment that joins the given points is given by: (-5/2,-5) .

In the question ,

it is given that ,

the points given is (3/5 , 4/5)

(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 = 1

that is

9/25 + 16/25 = 1

25/25 = 1

1 = 1

hence proved that the point (3/5, 4/5) is on the unit circle .

(b)  The distance between (2, -5) and (-7, -5) is calculated using the formula

\(=\)√(x₂ - x₁)² \(+\) (y₂ - y₁)²

= √(-7 - 2)² + (-5 -(-5))²

= √(-9)² + (-5 + 5)²

= √(-9)² = √81

= 9 units

(c) the mid point joining the points (2, -5) and (-7, -5) is (a,b) that is calculated by

a = (2-7)/2     ,   b = (-5-5)/2

a = -5/2        ,     b = -10/2

a = -5/2 and b = -5

the mid point is (-5/2,-5)  .

Therefore , (a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .

(b) The distance between points (2, -5) and (-7, -5) is 9 units  .

(c) The midpoint of the line segment that joins the given points is given by (-5/2,-5)  .

The given question is incomplete , the complete question is

(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² =        .

(b) The distance between (2, -5) and (-7, -5) is         .

(c) The midpoint of the line segment that joins the given points is given by  (     ,     )    .

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Answer:2

Step-by-step explanation:

I’m not exactly sure bc I’ve never heard a problem like that before but I believe that’s correct.

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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Step-by-step explanation:

the slope is (y coordinate change / x coordinate change) when going from on point on the line to another.

it does not matter in what direction we go, but it is important to keep the same direction for the x and for the y comparison.

so, because I prefer to go from left to right, let's go from

(-16, 8) to (-3, -4) :

x changes by +13 (from -16 to -3).

y changes by -12 (from 8 to -4).

so, the slope is

-12/+13 = -12/13

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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Answer:

Step-by-step explanation:

two

Considering the volume of a rectangular prism, since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

The volume of a rectangular prism of length l, width w and height h is given by:

V = lwh.

The original dimensions are:

h = 7.9 cm, l = 3 cm, w = 1.5.

Hence the volume in cm³ was:

V = 7.9 x 3 x 1.5 = 35.55 cm³.

The infuser was filled to 80% capacity, hence:

Vf = 0.8 x 35.55 = 28.44 cm³.

For the new dimensions, we have that h = 7 cm, hence the volume is:

Vn = 7 x 3 x 1.5 = 31.5 cm³.

28.44/31.5 x 100% = 90.29%.

Since the new volume is greater than the filled volume, the new dimensions would work, and 90.29% of the infuser would be filled.

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Answer:

0.90 seconds

Step-by-step explanation:

We will see that one complete revolution takes (2π/7) seconds.

Here we have the function:

f(x) = 33sin(7x−π/12) + 33

The time needed to do a full revolution is given by the period of the function.

Remember that:

sin(x) = sin(x + 2π).

Then:

sin(7x−π/12) = sin(7*(x + T) −π/12)

Then we must have:

2π = 7*T

Where T is the period.

Solving for T, we have:

2π/7 = T

This means that one complete revolution takes (2π/7) seconds.

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The equation of the line;

Problem statement

Write the equation of the line; with the given properties, in slope-intercept form.

Slope (m)= -5 through (-5, 5)

Solution

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the

y-intercept.

Since (-5, 5 ) is a point on the line, we can "plug in" -5 for x and 5 for y into our equation to obtain

We now substitute for b now

The equation of the line;

Robert's time was 3 hours, and Wilbur's time was 1 hour and 30 minutes.

To determine the time taken by Robert and Wilbur, we need to use the formula:

Time = Distance / Speed

Since both Robert and Wilbur covered the same distance, we can equate their respective time formulas:

Distance / Robert's Speed = Distance / Wilbur's Speed

Simplifying the equation, we find:

Robert's Speed / Wilbur's Speed = Wilbur's Time / Robert's Time

Given that Robert's speed was 6 miles per hour and Wilbur's speed was 8 miles per hour, we can substitute these values into the equation:

6 / 8 = Wilbur's Time / (Wilbur's Time + 2)

Cross-multiplying and solving for Wilbur's Time, we get:

8(Wilbur's Time) = 6(Wilbur's Time + 2)

8Wilbur's Time = 6Wilbur's Time + 12

2Wilbur's Time = 12

Wilbur's Time = 6

Since Wilbur's time was given in hours and minutes, we convert 6 hours into 6 hours and 60 minutes. Therefore, Wilbur's time is 1 hour and 30 minutes.

To find Robert's time, we add 2 hours to Wilbur's time:

Robert's Time = Wilbur's Time + 2

Robert's Time = 1 hour and 30 minutes + 2 hours

Robert's Time = 3 hours

Thus, Robert's time was 3 hours, and Wilbur's time was 1 hour and 30 minutes.

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Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

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