Math question 7 help

The area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

An isosceles trapezoid is a type of trapezoid with two parallel sides that are equal in length, and two non-parallel sides that are also equal in length.  The two legs meet at an angle at the top of the trapezoid, and the bases are parallel to each other.

To find the area of the trapezoid, we use the formula:

Area = (b1 + b2) * h / 2

where b1 and b2 are the lengths of the bases, and h is the height.

In this case, b1 = 9, b2 = 21, and h is the distance between the bases. Since the trapezoid is isosceles, the height is also the length of the two diagonals minus the sum of the two bases, divided by 2:

h = (d1 + d2 - b1 - b2) / 2

we will use the Pythagorean theorem:

d1² = h² + (b2 - b1/2)²

d2² = h² + (b2 + b1/2)²

Plugging in the values we get:

h = (d1 + d2 - 9 - 21) / 2

h = (d1 + d2 - 30) / 2

d1² = h² + (21 - 9/2)²

d2² = h² + (21 + 9/2)²

Simplifying, we get:

h = (d1 + d2 - 30) / 2

d1² = h² + 225/4

d2² = h² + 529/4

Substituting the first equation into the other two, we get a system of two equations in two variables:

d1² = ((d1 + d2 - 30) / 2)² + 225/4

d2² = ((d1 + d2 - 30) / 2)² + 529/4

Simplifying and solving for d1 and d2, we get:

d1 = 13

d2 = 17

To find the area, we plug in the values of the bases and the height:

h = (d1 + d2 - 30) / 2 = (13 + 17 - 30) / 2 = 5

Area = (b1 + b2) * h / 2 = (9 + 21) * 5 / 2 = 75

Therefore, the area of the trapezoid is 75 square units, and the lengths of the diagonals are 13 and 17 units.

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When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

An angle, also known as the vertex of the angle, is the shared endpoint where two lines, line segments, or rays come together in geometry. Angles are commonly expressed as degrees or radians. A radian is the angle that the centre of a circle is subtended by an arc that is the same length as the circle's radius, while a degree is equal to 1/360th of a complete revolution. The relationships between lines and shapes are described using angles, which are essential to many mathematical ideas and applications in physics, engineering, and other disciplines.

given

Trigonometry can be used to resolve this issue. Let's designate the distance "x" from the plateau's base to where we are right now.

We must first determine the height we are at right now. Since we are aware of the slope angle, we can accomplish this using the tangent function:

tan(20°) Means adjacent/opposite

h is the height we are presently at, so tan(20°) = h/x.

To find h, we can change this equation as follows:

h Equals x * tan(20°)

x² + h² = 40^2

If you replace h = x * tan(20°):

x² + (x*tan(20°))

x² = 40²

Simplifying:

x² + 0.364x²= 1600

1.364x² = 1600

x² = 1171.61

x ≈ 34.22

When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

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The height of the person after 4 seconds is -48 meters. Below you will learn how to solve the problem.

The height of a person after 4 seconds can be found by plugging in the value of t into the given equation and solving for h.

Step 1: Plug in the value of t into the equation:
h = 2 * (4 - 5) ^ 2 - 50

Step 2: Simplify the equation:
h = 2 * (-1) ^ 2 - 50

Step 3: Simplify further:
h = 2 * 1 - 50

Step 4: Solve for h:
h = 2 - 50

Step 5: Simplify to get the final answer:
h = -48

Therefore, the height of the person after 4 seconds is -48 meters.

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The estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F

The range rule of thumb is used to estimate the standard deviation of a data set using the range of the data. In this case, the range of the data is 3.5 degrees F. Using the range rule of thumb, the standard deviation of the data can be estimated by taking the range (3.5) and dividing it by 4, which gives us an estimated standard deviation of 0.875 degrees F.

This estimated value is within 0.2 degrees F of the actual standard deviation of the data (0.72 degrees F).

To compare this result to the actual standard deviation of the data, we subtract the estimated value from the actual value and take the absolute value of the result. This gives us the difference between the two values:

|0.72 - 0.875| = 0.155

Since the difference between the estimated and actual standard deviations is less than 0.2 degrees F, we can say that the range rule of thumb provides a reasonable approximation of the standard deviation for this data set.

In conclusion, the estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F, and this value is within 0.2 degrees F of the actual standard deviation of 0.72 degrees F.

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The distribution is  X ~ N(46, 19), the probability that a randomly selected student's time will be between 42 and 44 minutes is 0.04147. the probability that the average time studying for the 50 students is between 42 and 44 minutes is 0.1601.

a. X ~ N(46, 19)

b. e is not defined in the problem, so it does not have a distribution.

c. z ~ N(0, 1) (standard normal distribution)

d. To find the probability that one randomly selected student's time will be between 42 and 44 minutes, we first standardize the values:

z = (44 - 46) / 19 = -0.1053

z = (42 - 46) / 19 = -0.2105

Using a standard normal table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(-0.2105 < z < -0.1053) = 0.04147

Therefore, the probability that a randomly selected student's time will be between 42 and 44 minutes is 0.04147.

e. To find the probability that the average time studying is between 42 and 44 minutes, we need to use the central limit theorem. Since we have a large enough sample size (n = 50) and the population standard deviation is known, we can use the following formula to standardize the sample mean:

z = (x - μ) / (σ / √n)

Substituting the given values:

z = (44 - 46) / (19 / √50) = -0.7443

z = (42 - 46) / (19 / √50) = -1.4886

Using a standard normal table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(-1.4886 < z < -0.7443) = 0.1601

Therefore, the probability that the average time studying for the 50 students is between 42 and 44 minutes is 0.1601.

f. The total study time for the 50 students follows a normal distribution with mean 5046 = 2300 minutes and standard deviation √5019 ≈ 39.70 minutes. To find the probability that the total study time is more than 2200 minutes, we standardize the value:

z = (2200 - 2300) / 39.70 = -2.5189

Using a standard normal table or calculator, we can find the area under the standard normal curve to the right of this z-score:

P(z > -2.5189) = 0.99411

Therefore, the probability that the randomly selected 50 students will have a total study time more than 2200 minutes is 0.99411.

g. The assumption of normality is necessary for parts e) and f) because we are using the normal distribution and the central limit theorem to approximate the probabilities. Without the normal assumption, we would need to use different methods for probability calculations.

h. We need to find the least total time that corresponds to the top 15% of the distribution. Using a standard normal table or calculator, we can find the z-score that corresponds to the 85th percentile:

z = 1.0364

We can then use the formula for the total study time:

x = μ + z(σ / √n)

Substituting the given values:

x = 4650 + 1.0364(19*√50) ≈ 4652.78

Therefore, the least total time that a group can study and still receive a sticker is approximately 4652.78 minutes.

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There is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

Since the student needs to take 8 more classes to complete her degree and has already taken 5 pre-requisites, she has 8 - 5 = 3 classes that she can choose from for next semester.

To calculate the number of ways she can take 4 classes next semester, we can use the combination formula:

nCr = n / (r × (n-r))

where n is the number of classes she can choose from (which is 3), and r is the number of classes she will take next semester (which is 4).

Plugging in the values, we get:

3C4 = 3 / (4 × (3-4)) = 0

Since we cannot choose 4 classes from a set of 3 classes, the answer is 0.

Therefore, there is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.

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The value conversion of polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² to standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.

To rewrite the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² in standard form, we need to arrange the terms in decreasing order of their degree, with the highest degree term first.

Rewrite the polynomial with the terms in descending order of degree:

[tex]x^4[/tex] - 2x³ - x² + 1/7

Combine any like terms:

There are no like terms to combine in this polynomial.

Rewrite the polynomial in standard form:

The polynomial in standard form is:

[tex]x^4[/tex] - 2x³ - x² + 1/7

Therefore, the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x^2 in standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.

It is important to remember to always arrange the terms in descending order of degree when writing a polynomial in standard form.

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The series converges.

To test the series 3 + 3/5 + 3/5^2 + 3/5^3 + … =∑n=0[infinity] 3/5^n,

we can use the ratio test.

Specifically, we can look at the ratio of each successive term.

Let an+1/an = 3/5n+1/3/5n = 1/5. Since this is less than 1, the series converges.

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terms of time t.

A. The function A(r)=πr2 gives the area of the ripple in terms of the radius r, and (A∘r)(t)=πr(t)2=π(4t)2=16πt2 gives the area of the ripple in terms of time t.

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If Colin wants to make 2 batches of Lavender soap and 2 batches of Vanilla soap, then he will need $9.57 for the oils

Here, Colin needs 1.5 ounces of Scented oil to make a batch of soap.

He wants to make 2 batches of Lavender soap and 2 batches of vanilla soap.

So, the amount of scented oil for 2 batches would be:

1.5 × 2 = 3 ounces

The cost of an ounce of Lavender oil is $1.54

So, using unitary method the cost of oil for the 2 batches of Lavender soap would be:

C₁ = 3 × 1.54

C₁ = 4.62 dollars

The cost of an ounce of Vanilla oil is $1.65

So,  using unitary method the cost of oil for the 2 batches of Vanilla soap would be:

C₁ = 3 × 1.65

C₁ = 4.95 dollars

Thus, the total cost would be,

C = C + C

C = 4.62 + 4.95

C = 9.57 dollars

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The common factors are \[(x+5)\], so the LCM is (x+5)²(x+6) of the given polynomials. The Least Common Multiple (LCM) of the two given polynomials can be found by factoring them and then finding the common factors:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

To determine the LCM of the given polynomials, we need to factor each polynomial and then multiply the factors together, taking the highest power of each factor.

First, let's factor each polynomial:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

Now, let's find the LCM by multiplying the highest power of each factor together:

LCM = (x+5)(x+5)(x+6) = (x+5)²(x+6)

So, the LCM of the given polynomials is (x+5)²(x+6) in factored form.

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Answer:

35° and 55°

Step-by-step explanation:

(x - 20) and x form a right angle (90° ) and are complementary

complementary angles sum to 90° , then

x - 20 + x = 90

2x - 20 = 90 ( add 20 to both sides )

2x = 110 ( divide both sides by 2 )

x = 55

then the 2 angles are

x = 55°

x - 20 = 55 - 20 = 35°

Step-by-step explanation:

the area of the full larger circle minus the area of the smaller circle.

the area of a circle is

pi×r²

the radius of the smaller circle is 23.1 yd.

the radius or the larger circle is 23.1 + 7.8 = 30.9 yd.

the area of the larger circle is

pi×30.9² = 3.14 × 954.81 = 2,998.1034 yd²

the area of the smaller circle is

pi× 23.1² = 1,675.5354 yd²

the area of only the ring around the smaller circle is then

2,998.1034 - 1,675.5354 = 1,322.568 yd² ≈

≈ 1,322.57 yd²

or

pi×30.9² - pi×23.1² = pi(954.81 - 533.61) =

= 421.2pi = 421.2 × 3.14 =

= 1,322.568 ≈ 1,322.57 yd²

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

a. x = 11; mAB = 34°

b. x = 25.5; mAB = 46°

c. x = 17; mAB = 46°

d. x = 11; mAB = 17

Step-by-step explanation:

Step-by-step explanation:

Refer to pic............

Answer:

  x = 10.1

Step-by-step explanation:

You want the value of x in the given secant-tangent geometry.

The angle between the secant ON and the tangent MN is half the measure of arc ON. The measure of arc ON is the remainder of the circle after long arc ON = 283° is subtracted:

  arc ON = 360° -283° = 77°

  (5x -12)° = 1/2(77°) . . . . . relation of angle to arc

  10x -24 = 77 . . . . . . . . divide by °, multiply by 2

  10x = 101 . . . . . . . . . . add 24

  x = 10.1 . . . . . . . . . . divide by 10

The answer should be 10 1/2 ft

Here is my work below:

Answer: 1 1/4

Step-by-step explanation:

1/4 * 3 = 3/4

3/4 + 1/2 =

3/4 + 2/4 = 5/4 = 1 1/4

We can use trigonometry to solve this problem.

Let's call the distance we are looking for "x". We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse:

sin(51°) = opposite/hypotenuse

We know that the hypotenuse is the length of the ladder, which is 3.8m. We can solve for the opposite side (x) by rearranging the equation:

x = sin(51°) * 3.8m

x ≈ 2.98m

So the bottom of the ladder is about 2.98 meters away from the wall. Rounded to the nearest tenth, the answer is 3.0 meters.

the answer to the question Simplify. Express your answer z^(4)*z*z" is z^(6).

To simplify the expression z^(4)*z*z, we need to use the rules of exponents. Specifically, we need to use the rule that states that when we multiply expressions with the same base, we can add the exponents. In other words, a^(b)*a^(c) = a^(b+c).

Using this rule, we can simplify the given expression as follows:

z^(4)*z*z = z^(4+1+1) = z^(6)

So, the simplified expression is z^(6).

In conclusion, the answer to the question "Simplify. Express your answer z^(4)*z*z" is z^(6).

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6%=300

300 x 5 = 1500

5k add £1500

=

6500

Answer:Next year, he will have 5% more than that. To find our total value at the end of the year, .

Step-by-step explanation:

Coordinates of the vertices of the pre-image are (-4, 4), (-1, 9), and (1, 9).

And the graph is given below.

A transformation of a triangle can refer to any process that changes the size, position, or shape of a triangle.

Translation involves moving the triangle without changing its shape or size. To translate a triangle, you can simply move it in any direction by a certain distance, without rotating or flipping it.

Here we have

From the graph

The coordinates of the triangle are (1, 1) (4, 6), and (6, 3)

Given T < -5, 3 > (x, y)

Hence, the coordinates of the pre-image are

(1, 1) => (1 - 5,  1 + 3)  = (-4, 4)  

(4, 6) => (4 - 5, 6 + 3) = (-1, 9)

(6, 3) => (6 - 5,  3+3) = (1, 6)

Hence,

Coordinates of the vertices of the pre-image are (-4, 4), (-1, 9), and (1, 9).

And the graph is given below.

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The product of the two given binomials can be expressed as the trinomial 2561104x³ + 684636x² + 87719x + 736, which is in its simplest form.

In this case, we will multiply the first two binomials (12x+1)(21x+1) and then multiply the second two binomials (65x+32)(56x+23). We will then multiply the two resulting expressions to get the final trinomial.

To multiply (12x+1)(21x+1), we can use the distributive property of multiplication, which states that a(b+c) = ab + ac. Therefore, we have:

(12x+1)(21x+1) = 12x(21x) + 12x(1) + 1(21x) + 1(1) = 252x² + 12x + 21x + 1 = 252x² + 33x + 1

Similarly, to multiply (65x+32)(56x+23), we have:

(65x+32)(56x+23) = 65x(56x) + 65x(23) + 32(56x) + 32(23) = 3640x² + 1495x + 1792x + 736 = 3640x² + 3287x + 736

Now, to find the product of the two expressions, we can multiply them using the distributive property again:

(252x² + 33x + 1)(3640x² + 3287x + 736) = 252x²(3640x²) + 252x²(3287x) + 252x²(736)

   • 33x(3640x²) + 33x(3287x) + 33x(736)

   • 1(3640x²) + 1(3287x) + 1(736)

Simplifying this expression by combining like terms, we get:

= 917280x⁴ + 1573824x³ + 684636x² + 87719x + 736

This final expression has four terms, but it can be simplified further to a trinomial by combining the first two terms using the associative property of addition. We have:

917280x⁴ + 1573824x³ + 684636x² + 87719x + 736 = (917280x⁴ + 1573824x³) + (684636x² + 87719x + 736) = 2561104x³ + 684636x² + 87719x + 736

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Complete Question:

Express the product of(12x+1)(21​x+1) and(65x+32)(56​x+23​) as a trinomial in simplest form

The requried equation represents the volume of the gas in terms of temperature is V = 22 + 225T.

The equation model is defined as the representative of the given case in the form of an equation using variables and constants.

Here,
Let's denote the volume of the gas as V and temperature as T.

From the given information, we know that at 0°C temperature (i.e. T = 0), the volume of the gas is 22 liters.

For every 1°C increase in temperature, the volume of the gas increases by 225 liters.

Therefore, we can write the equation as:

V = 22 + 225T

This equation represents the volume of the gas in terms of temperature.

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Answer: See attached.

Step-by-step explanation:

    Since the first equation uses a ≤ symbol, we know we will use a solid line. This is because it is less than and equal to. Then, we will graph it as a regular slope-intercept line.

    This line has a slope of 5 and a y-intercept of -2. This means we will start at (0, -2) and move five units up for every unit right, or five units down for every unit left.

    For the next equation, it uses a > symbol so we will use a dashed line. This is because it is not equal to, only greater than. Same as the previous. We will graph it as a slope-intercept line, but using a dashed line instead of a solid line.

    This line has a slope of -2 and a y-intercept of positive 5. This means we will start at (0, 5) and move two units down for every unit right, or two units up for every unit left.

The hypothesis of this research is that there is a positive correlation between the independent variables (hours slept on the night of the test, hours spent studying the week before the test, and student's IQ) and the dependent variable (test scores). As such, the null hypothesis states that there is no relationship between the independent variables and the dependent variable, while the alternative hypothesis states that there is a relationship between the independent variables and the dependent variable. Symbolically, this can be written as:

H0: There is no relationship between the independent variables and the dependent variable

H1: There is a relationship between the independent variables and the dependent variable

Given the hypothesis, the independent variable (number of hours of sleep, number of hours spent studying, and IQ) are quantitative and discrete, and the dependent variable (test scores) is ratio, an f test is the most appropriate statistical test to use. An f test will allow us to compare the independent variables to see if there is a statistically significant difference between the independent variables and the dependent variable. By using an f test, we can determine if the independent variables are actually associated with the dependent variable and how strong that association is.

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Answer:

9*5*7 = 315 week

9*5 = 40 day

Step-by-step explanation:

hope it helps

Answer:

9 songs/day × 5 days = 45 songs/day

45 songs/day × 7 days/week = 315 songs this week

$120,000

The formula for an exponential function passing through the points (-2,--) and (2, 75) is: y = 75 * 2x + 2. To answer the question about the house valued at $120,000, the value of the house is not related to an exponential function. Therefore, the answer is that the value of the house is $120,000.

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