Shureka Washburn has scores of 67, 65, 64, and 88 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 73 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).

Assume that the number of granola bars is x and the number of bottles is y

Since they decided to purchase at least 50 bottles

At least means greater than or equal, so

Since the cost of 1 bar = $0.50, then

The cost of all bars = 0.50x

Since the cost of 1 bottle = $0.75, then

The cost of all bottles = 0.75y

Since their budget is $75

They can not exceed that, then

The solution will be in the common part of the two colors

The red represents the second inequality

The blue represents the first inequality

Answer:

the set of all real numbers -1≤y≤1

Step-by-step explanation:

according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.

Answer:

$3,795.96

Step-by-step explanation:

Base amount: $3,000.00

Interest Rate: 4% (yearly)

Effective Annual Rate: 4%

Calculation period: 6 years

Answer:

Step-by-step explanation:

Hey, do you mean what is the final charge? If so, then look at my next steps

If you mean the final charge then first multiply 10% by 360 , basically 10/100 multiplied by $360 which is equals to $36. Since it is interest, add $36 to $360. The answer will be $396. Then you add on the $19 which would bring the total to $415.

Hehe I am no expert but this is what I did . Tried my best

Answer:

C

Step-by-step explanation:

3:4

4:3

and the dots are 4:3

The measures of the angles are:

m ∠GAL = 90°

m ∠LAO = 71°

m ∠CAO = 109°

m ∠KAC = 71°

From the question, we are to determine the measure of the angles

m ∠GAL = 90° (Right angle)

m ∠LAO

m ∠LAO + m ∠GAL + 19° = 180° (Sum of angles on a straight line)

m ∠LAO + 90° + 19° = 180°

m ∠LAO = 180° - 90° - 19°

m ∠LAO = 90° - 19°

m ∠LAO = 71°

m ∠CAO

m ∠CAO = m ∠KAL (Vertically opposite angles)

m ∠KAL = m ∠GAL + 19°

m ∠KAL = 90° + 19°

m ∠KAL = 109°

Therefore,

m ∠CAO = 109°

m ∠KAC = m ∠LAO (Vertically opposite angles)

m ∠LAO = 71°

Therefore,

m ∠KAC = 71°

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Answer:

0.1056

0.2642

Step-by-step explanation:

N = 400

P = 10%

n*p = 400*0.1 = 40

n(1-p) = 400 * 0.9 = 360

40 and 360 are greater than 5 so we use the normal distribution here to estimate further.

mean = n*p = 40

sd = \(\sqrt{np(1-p)}\)

\(\sqrt{400*0.1(1-0.1)} \\= \sqrt{40(0.9)} \\= \sqrt{36} \\= 6\)

p(X≥48)

= p(X≥47.5)

\(=P(Z<\frac{47.5-40}{6} )\\= P(Z<1.25)\)

= 0.8944

1 - 0.8944

= 0.1056

FOR Y

N = 400 p = 0.25% = 0.0025

400 * 0.0025 = 1

1 is less than 5 so we use poisson distribution.

using the excel function,

1 - BINOMDIST(1, 400, 0.0025, TRUE)

= 1 - 0.735759074

= 0.2642

Answer:

d=6

Step-by-step explanation:

d+7=13

  -7  -7

-----------

d=6

Answer:

hi

Step-by-step explanation:

\(d + 7 = 13 \\ d = 13 - 7 \\ d = 6\)

have a nice day bye

Answer:

x=19

Step-by-step explanation:

-4 (5 - x) + 7x = 189  Distribute

4x-20+7x=189   Combine Like Terms

11x-20=189 Add 20 To Both Sides

11x=209 Divide By 11

x=19

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).  Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.

To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.

The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.

Now, we can substitute the values into the formula:

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).

Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

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Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Answer: Choice 1

3(MC) = SC

=====================================================

Explanation:

The three medians intersect at the centroid, which is point M in this case. The intersecting medians subdivide themselves in the ratio 2:1

This means that SM is twice as long as MC. We can say SM = 2MC

Then by the segment addition postulate, we know that:

SC = SM + MC

SC = 2MC + MC

SC = 3MC

3(MC) = SC

So having three copies of MC glued together will form segment SC.

The same idea applies for the other medians also (EK = 3EM and RL = 3ML).

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

Answer:

Domain: \(x\geq 0\)

Range: \(y\leq 0\)

Step-by-step explanation:

Recall that the domain of a function is the values that x can be, while the range of a function is the values that y can be.

Let's take a look at one part of the function: \(\sqrt{x}\).

The square root of any positive number does exist. It may not be rational, but it exists. The square root of zero also exists -- it's zero.

However, the square root of a negative number will never exist - it's imaginary. So, x cannot be negative as long as it is under the radical.

The domain is: \(x\geq 0\)

Now, to find the range, let's look at the coefficient: -3.

A negative number times a negative number is positive. A negative number times a positive number is negative.

However, x can never be negative, so no matter what real value you plug in for x, you will always be multiplying -3 by a positive number (or zero).

Since zero times any number is zero, and a positive number times a negative number is a negative number, y will always be either equal to zero or negative.

So, the range is: \(y\leq 0\)

Answer:

\( < 6. - 10 > \)

<6,-10>

add themmm

If the base triangle has a base of 8 meters and a height of 6.9 meters. the surface area of the pyramid is 139.6 square meters.

First, let's find the area of the base triangle:

Area of base triangle = (1/2) * base * height

Area of base triangle = (1/2) * 8 * 6.9

Area of base triangle = 27.6 square meters

Now, let's find the area of one of the triangular faces:

Area of triangular face = (1/2) * base * height

Area of triangular face = (1/2) * 8 * 7

Area of triangular face = 28 square meters

Since the pyramid has four triangular faces, the total area of the triangular faces is 4 times the area of one triangular face, which is:

4 * 28 = 112 square meters

Total surface area = area of base triangle + area of triangular faces

Total surface area = 27.6 + 112

Total surface area = 139.6 square meters

Therefore, the surface area of the pyramid is 139.6 square meters.

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Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

In this case,

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

--------------

====================================================

Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

--------------

Answer:

A). \(\frac{1.8}{6} = \frac{height}{60}\)

B). 18 meters tall

Step-by-step explanation:

We see TWO right triangles in this problem:

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

\(\frac{1.8}{6} = \frac{height}{60}\)

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

Option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, is the same as 12.8.

It is defined as the combination of constants and variables with mathematical operators.

The options are:

A: -3 - 4.9x = 12.8

B: 4.9x - (-3) = 12.8

C: 3+ 4.9x = 12.8

D: (4.9 - 3)x = 12.8

E: 12.8 = 4.9x + 3

We have a statement:

Negative 3 less than 4.9 times a number, x, is the same as 12.8.

We can write in a mathematical form:

4.9x - (-3) = 12.8

or

4.9x + 3 = 12.8

or

12.8 = 4.9x + 3

Thus, option B, option C, and option E are correct because the equation is Negative 3 less than 4.9 times a number, x, is the same as 12.8.

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The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression

Given data ,

Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:

( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ

Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.

So , on simplifying the equation , we get

= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²

= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²

= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²

Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.

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When in a right angle triangle, the right angle has two angles inside it i.e. x+4° and  3x+2°, x is equal to 21.

what exactly is a triangle?

A triangle is a three-sided polygon, which is a two-dimensional shape with straight sides. It is one of the simplest and most common geometric shapes in mathematics. A triangle is defined by its three sides and three angles.

The total sum of the angles of a triangle is always equal to 180 °. The length of the sides and the size of the angles can vary, giving rise to different types of triangles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles.

Now,

The sum of two adjacent angles inside a 90° angle is 90°. So, we can set up an equation:

x + 4 + 3x + 2 = 90

Simplifying the left side by combining like terms:

4x + 6 = 90

Subtracting 6 from both sides:

4x = 84

Dividing by 4:

x = 21

Therefore, The value of  x is 21.

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The ruler postulate is that A. the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.

The set of points on a line can be arranged in such a way that the set of real numbers and the set of points correspond exactly, and the distance between any two points is equal to the absolute value of the difference between the corresponding numbers.

Therefore, the ruler postulate is that the distance between two points can be determined by the absolute value of the difference of the real number values of the two points.

In conclusion, the correct option is A.

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Answer:

Number 1 does not represent a function because it does not pass the Vertical Line Test.

Number 2 does not represent a function because it does not pass the Vertical Line Test.

Answer: Without a visual representation of the triangles, it's difficult to determine whether the statements are true or false.

However, in general, the side lengths of a triangle determine its shape and size. If two triangles have the same side lengths, then they are congruent, meaning they have the same shape and size. Therefore, if the triangles in question have different side lengths for x = 16, x = 27, and x = 31, then it's possible that the statements are either true or false, depending on the specific side lengths.

Without additional information, it's not possible to determine whether the statements are true or false.

Step-by-step explanation:

Answer:

The probability of an event occurring depends on the sample space and the frequency of the event

permutations and combination principles would have to be applied to determine the probability of a particular number showing up when a pair of dice is rolled ,while a single dice roll have a fixed frequency of every event ( 1,2,3,4,5,6,) hence probability of a number showing up is 1/6

Step-by-step explanation:

The probability of an event occurring depends on the sample space and the frequency of the event

The  total outcomes of rolling a pair of fair dice would be = ( total outcome of  single dice A * total outcome of  single Dice B ) = 6 * 6 = 36. and this is because the Two dice are independent of each other. hence there is a higher variability in the determining the possibility of a particular number ( 1,2,3,4,5,6) showing up when a pair of dice is rolled due to the larger sample space. permutations and combination principles would have to be applied to determine the probability of a particular number showing up when a pair of dice is rolled ,while a single dice roll have a fixed frequency of every event ( 1,2,3,4,5,6,) hence probability of a number showing up is 1/6

The circles in the figures form a series

The next step in the series is (B)

From the figure, we have the following highlights

Using the above pattern, the next circle must have 6 segments

Hence, the next step in the series is (B)

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The answer to all parts is shown below.

1. The most useful statistical instrument to be used with a big number of respondents is a survey questionnaire.

This allows researchers to collect data from a large sample size efficiently and in a standardized manner, ensuring that all respondents are asked the same questions in the same order. Online surveys are particularly useful as they can reach a wider audience and allow for easy data analysis.

2. The process you are referring to is called "expert interviews".

3. This is an example of a survey question that measures a respondent's preference.

4. The changes in characteristics, behavior, and attitudes of the people observed are the focus of observation.

5. Open-ended question.

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The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

At any time, there are about 29.4 users on the developer's site

Little's law states that: If users log on to a website at an average rate of

r users per minute and each stays on the site for an average time of T minutes, the average number of users on the website, N, at any one

time is given by the formula N= rT

Given that:

196 users per hour log on to a site

Each user spends an average of 9 minutes on the site

This implies:

r = 196 users per hour =  196/60  = 49/15 users per minute

T = 9 minutes

N = rt

N = 49/15 × 9

N = 29.4 users

Therefore, at any time, there are about 29.4 users on the developer's site

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