11. Find the exact value for each expression. a) cos80°cos 20° + sin80°sin 20° d) tan105°

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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Answer:

71

Step-by-step explanation:

82 plus 27=109

180-109=71

Answer:

64 left handed girls

25 left handed boys

89 total left handed students

Step-by-step explanation:

Multiply 320 x 0.2

Multiply 250 x 0.1

You can think of it this way, 0.2 is 2/10 and 0.1 is 1/10 so take 20 percent of 320 and 10 percent of 250

Add them up for your answer 64 + 25 = 89

The only difference for these devices in 3701 is that the jk-FF (or jk-latch) has an additional control input, which is the clock (CK). The CK input is used to enable and disable the device so that the inputs, j and k, do not always affect the output (Q) of the device.

The SR-FF (or SR-latch) has two inputs, S and R, which directly affect the output, Q. When S=1, the output is set to 1, and when R=1, the output is reset to 0.

On the other hand, the jk-FF (or jk-latch) has three inputs, J, K and CK. When CK is 0, the device is disabled and the outputs remain the same. When CK is 1, the J and K inputs can be used to either set (J=1, K=0) or reset (J=0, K=1) the output, Q.

In summary, the j and k in the jk-FF (or jk-latch) are similar to the s and r in the SR-FF (or SR-latch).

So, the only difference is the addition of a clock (CK) input in the jk-FF (or jk-latch). This clock (CK) input enables and disables the device, which allows the inputs, j and k, to affect the output (Q) of the device.

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Answer: True

Step-by-step explanation: because bias can lead to personal errors

Answer:

first angle is 95

second angle is 95

third angle is 95

the sum of angle in a quadrilateral is 360

therefore 95+95+95°=285

to get the fourth angle=360-285=75

therefore the fourth angle is 75°

Omar should go back and regroup the terms in step 1 as (3x^3 – 15x^2) – (4x + 20). In step 2, Omar should factor only out of the first expression.

When factoring polynomials, it is essential to look for common factors that can be factored out. In this case, Omar noticed that there are no common factors in the given polynomial. To proceed, he should go back and regroup the terms in step 1 as (3x^3 – 15x^2) – (4x + 20).

This regrouping allows Omar to factor out of the first expression, which can potentially lead to further factoring or simplification. However, without additional information about the polynomial or any specific instructions, it is not possible to determine the exact steps Omar should take after this point.

In summary, regrouping the terms and factoring out of the first expression is a reasonable next step for Omar to explore the polynomial further.

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Reptile stickers come in sheets of 6 and Marine Life stickers come in sheets of 9 .

Number of reptile sticker = 6

Number if marine sticker = 9C

Answer:

2.79 mi/hr    ( for the time they were actually moving)

Step-by-step explanation:

average speed = total distance / total time

                      = ( 10.4 + 8.6 mi) / ( ( 181 + 227 min )/60 min/hr) =2.79 mi/hr

The integer values of x that satisfy the inequality 3x - 3 > 12 are 6, 7, 8, 9, 10

To solve the inequality 3x - 3 > 12, we can isolate the variable x on one side of the inequality by adding 3 to both sides:

3x - 3 + 3 > 12 + 3

3x > 15

Next, we can divide both sides by 3 to get x by itself:

x > 5

So we know that any integer value of x in the interval [4, 10] that is greater than 5 will satisfy the inequality.

Therefore, the integer values of x that satisfy the inequality are:

6, 7, 8, 9, 10

Note that 5 is not included in this list, since the inequality is strict (i.e., x is greater than 5, not greater than or equal to 5).

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Option C and Option D has infinite number of solutions

Option A: -2(x - 2) + 3x = x - 4

Simplify the equation;

-2x + 4 + 3x = x - 4

x + 4 = x - 4

LHS ≠ RHS

Thus, equation does not have infinite solutions.

Option B: 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)

Simplify the equation;

2x + 4x - 4 = 6x + 3 - 2x + 2

6x - 4 = 4x + 5

6x - 4x = 5 + 4

2x = 9

Obtained equation has only one solution.

Thus, equation does not have infinite solutions.

Option C: 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4

Simplify the equation;

3x + 2x - 4 + 6 = 4x + 6 + x - 4

5x + 2 = 5x + 2

LHS =RHS

Thus, this equation has infinite solutions.

Option D: 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)

Simplify the equation;

4x + 8 + x + 1 = 2x - 3 + 3x + 12

5x + 9 = 5x + 9

LHS =RHS

Thus, this equation has infinite solutions.

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The correct question is-

Which equations have an infinite number of solutions?

Select all that apply.

A -2(x - 2) + 3x = x - 4

B 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)

C 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4

D 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)

Answer:

180

Step-by-step explanation:

25% of 240 is 60 so then you subtract 60 from 240 witches is 180

Total number of spoon used in current month is 180 tablespoon

Number of percentage less used = 25%

Total number of spoon used last month = 240 tablespoon

Total number of spoon used in current month

Total number of spoon used in current month = Total number of spoon used last month[1 - 25%]

Total number of spoon used in current month = 240[1 - 0.25]

Total number of spoon used in current month = 240[0.75]

Total number of spoon used in current month = 180 tablespoon

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The probability that 4 or more patients out of 6 will benefit from the drug is approximately 0.256, or 25.6%.

To calculate the probability that 4 or more patients will benefit from the drug out of 6 patients who take it, we can use the binomial probability formula. Let's break down the steps to determine this probability:

The drug is reported to benefit 40% of the patients who take it. This means that the probability of a patient benefiting from the drug is 0.40, or 40%.

We want to find the probability that 4 or more patients out of 6 will benefit from the drug. To do this, we need to calculate the probability of 4, 5, and 6 patients benefiting, and then sum those probabilities.

We can use the binomial probability formula to calculate these probabilities. The formula is given by P(X = k) = (nCk) * p^k * (1 - p)^(n - k), where P(X = k) is the probability of getting exactly k successes, n is the total number of trials, p is the probability of success, and (nCk) is the binomial coefficient.

Let's calculate the probability of 4 patients benefiting from the drug. Using the binomial probability formula:

P(X = 4) = (6C4) * (0.40)^4 * (1 - 0.40)^(6 - 4)

Simplifying the calculation:

P(X = 4) = 15 * (0.40)^4 * (0.60)^2

Let's calculate the probability of 5 patients benefiting from the drug:

P(X = 5) = (6C5) * (0.40)^5 * (1 - 0.40)^(6 - 5)

Simplifying the calculation:

P(X = 5) = 6 * (0.40)^5 * (0.60)^1

Finally, let's calculate the probability of 6 patients benefiting from the drug:

P(X = 6) = (6C6) * (0.40)^6 * (1 - 0.40)^(6 - 6)

Simplifying the calculation:

P(X = 6) = 1 * (0.40)^6 * (0.60)^0

Now, we can calculate the probability that 4 or more patients will benefit by summing the individual probabilities:

P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6)

Substituting the calculated values:

P(X ≥ 4) = (15 * (0.40)^4 * (0.60)^2) + (6 * (0.40)^5 * (0.60)^1) + (1 * (0.40)^6 * (0.60)^0)

Simplifying the calculation:

P(X ≥ 4) = 0.1536 + 0.0768 + 0.0256

P(X ≥ 4) = 0.256

Therefore, the probability that 4 or more patients out of 6 will benefit from the drug is approximately 0.256, or 25.6%.

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Answer:

New cut off salary = 30,592

Step-by-step explanation:

Given:

Normal distributed mean = $37,000

Standard deviation = $5000

Cut off salary = 10%

Find:

New cut off salary

Computation:

Z - left tale value of 10% is -1.2816

Corresponding x-value using x = zs + u

New cut off salary = (-1.2816)(5,000) + 37,000

New cut off salary = -6,408 + 37,000

New cut off salary = 30,592

To use Stokes' theorem to evaluate the given vector field, we need to find the curl of the vector field and calculate the surface integral over the cone.

First, let's find the curl of the vector field f(x, y, z) = arctan(x^2yz^2)i + x^2yj + x^2z^2k.

The curl of a vector field F = P i + Q j + R k is given by the following formula:
curl F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, P = arctan(x^2yz^2), Q = x^2y, and R = x^2z^2.

Taking the partial derivatives, we get:
∂P/∂x = 0, ∂P/∂y = 2x^2z^2, ∂P/∂z = 2x^2yz^2
∂Q/∂x = 2xy, ∂Q/∂y = x^2, ∂Q/∂z = 0
∂R/∂x = 2xz^2, ∂R/∂y = 0, ∂R/∂z = 2x^2z

Now, substituting these values into the formula for the curl, we have:
curl f = (2x^2z^2 - 0)i + (0 - 2xz^2)j + (2xy - 2x^2yz^2)k
      = 2x^2z^2i - 2xz^2j + 2xyk

Next, we need to calculate the surface integral over the cone.

The surface integral can be evaluated using the formula:
∫∫S (curl f) · dS = ∫∫D (curl f) · (r_u × r_v) dA

Here, (r_u × r_v) is the cross product of the partial derivatives of the position vector r(u, v) with respect to the parameters u and v, and dA is the differential area element.

In this case, the cone is given by x = sqrt(y^2 + z^2), 0 <= x <= 2, and we can parameterize the surface as r(u, v) = u sqrt(1 + v^2) i + u v j + u sqrt(1 + v^2) k, where 0 <= u <= 2, -1 <= v <= 1.

Taking the partial derivatives of r with respect to u and v, we have:
r_u = sqrt(1 + v^2) i + v j + sqrt(1 + v^2) k
r_v = u v i + j + u v k

Now, calculating the cross product r_u × r_v, we get:
r_u × r_v = (v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k

Finally, substituting the values into the surface integral formula, we have:
∫∫S (curl f) · dS = ∫∫D (2x^2z^2i - 2xz^2j + 2xyk) · ((v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k) dA

Now, you can evaluate this surface integral to find the answer.

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Sam has 5 months to pay back the money to his mom.

In this problem, we are using the formula for simple interest, which is represented by the equation l = prt, where:

"l" represents the amount of interest in dollars

"p" represents the principle amount of money loaned in dollars

"r" is the interest rate as a decimal

"t" is the time in months the money was borrowed

We are given that the principle amount (p) is $100, the interest rate (r) is 0.05 (which is 5% expressed as a decimal), and the maximum interest amount (l) is $25.

To find the time (t) in months that Sam has to pay back the money, we need to rearrange the formula and solve for "t". We substitute the given values into the equation:

l = prt

25 = 100 * 0.05 * t

Simplifying the equation, we multiply the values:

25 = 5t

To isolate "t", we divide both sides of the equation by 5:

5t = 25

t = 25 / 5

t = 5

Therefore, Sam has 5 months to pay back the money to his mom.

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Answer:

When dividing by −2, he did not change the direction of the sign.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

whenever u divide by a negative number in inequality the sign always changes

Answer:

P = 35.98 cm

Step-by-step explanation:

The Perimeter of a shape is the distance around the outside of it. This semi-circle (half circle) has a straight part and the curved part. See image. The straight part is the diameter (distance through the center) it is double the radius that was given, 7 cm.

The circumference of a circle is the perimeter of the whole circle.

C = 2pi•r or pi•d

C = 2pi•7 = 14pi

But you only need half, so 14pi/2 is 7pi.

ADD the straight part and the curved part to get the whole distance around the shape

P = 14 + 7pi

P ~= 35.98 cm

See image

Note:-

Solved as the all of above is one question

Solution:-

2 ft above

Now

Angle be x

Apply Pythagorean theorem

\(\\ \rm\Rrightarrow tanx=\dfrac{10}{400}\)

\(\\ \rm\Rrightarrow tanX=\dfrac{1}{40}\)

\(\\ \rm\Rrightarrow tanX= 0.025\)

\(\\ \rm\Rrightarrow X=tan^{-1}(0.025)\)

\(\\ \rm\Rrightarrow X=1.432°\)

The average birthweight of a nonsmoker was between 1,000 and 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

Given,

What is the newborn's weight?

A newborn's body weight is referred to as birth weight. At birth, babies of European descent typically weigh between 2.5 and 4.5 kilograms, or about 3.5 kilograms on average. South Asian and Chinese babies typically weigh 3.26 kg.

Here,

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

However, there are some obvious disparities between the two groups' typical ranges of birth weights. Since there are fewer newborns in the lower weight groups, over half of neonates among nonsmokers (56 out of 115, 48.7%) had birth weights between 3,000 and 4,000 grams. Less infants are born in the heavier weight categories; 40 of the 74 newborns delivered to smokers, or 54% of them, had birth weights between 2,000 and 3,000 grams.

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Answer:

Answer in explanation section

Step-by-step explanation:

8(2x-14)+13=4x-27.       Given

16x-112+13=4x-27.          Distributive property

16x-99=4x-27.                 Simplify

14x-99=-27.                      subtract

14x=72.                             Subtract

x=36/7.                              Divide to get x

Answer:

a^2/3

Step-by-step explanation:

the numerator simplifies to 5a^3 and the bottom is 15a. we can use our exponent rules to subtract exponents, so it is 1/3(a^2). this simplifies to a^2/3.

Answer:

a^2

------

3

Step-by-step explanation:

5 a^3  / 15a

Simplify the numbers

5/15 = 1/3

Simplify the variables

a^3 /a = a^2

Putting it back together

a^2

------

3

The margin of error for a 95% confidence interval can be calculated using the formula: Margin of error = (z-score) x (standard deviation)

where the z-score is the number of standard deviations corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard deviation is calculated as:
Standard deviation = sqrt[(population proportion) x (1 - population proportion) / sample size]
We know from the given information that the lower limit of the 95% confidence interval is 62% and the upper limit is 73.1%. Therefore, the midpoint of the interval is:
Midpoint = (lower limit + upper limit) / 2 = (62% + 73.1%) / 2 = 67.55%
Using this midpoint as an estimate for the population proportion, we can solve for the standard deviation:
Standard deviation = sqrt[(0.6755) x (1 - 0.6755) / n]
where n is the sample size (which is not given). Since we don't know the sample size, we can't calculate the standard deviation directly. However, we can use the fact that the margin of error is half the width of the confidence interval to estimate the sample size:
Margin of error = (upper limit - lower limit) / 2
Plugging in the given values, we get:
Margin of error = (73.1% - 62%) / 2 = 5.55%
Now we can solve for the standard deviation:
Standard deviation = sqrt[(0.6755) x (1 - 0.6755) / (sample size)]
Using the margin of error as an estimate for the standard deviation, we can solve for the sample size:
5.55% = 1.96 x sqrt[(0.6755) x (1 - 0.6755) / (sample size)]
Solving for sample size, we get:
sample size = 610.05
Rounding up to the nearest whole number, we get a sample size of 611. Therefore, the margin of error for this 95%confidence interval is approximately 5.55%, assuming a sample size of 611.

Given a 95% confidence interval for a population proportion with limits (62%, 73.1%), you are asked to find the margin of error.
Step 1: Calculate the midpoint of the interval.
Midpoint = (Lower limit + Upper limit) / 2
Midpoint = (62% + 73.1%) / 2
Midpoint = 135.1% / 2
Midpoint = 67.55%
Step 2: Determine the margin of error.
Margin of error = (Upper limit - Midpoint) or (Midpoint - Lower limit)
Margin of error = (73.1% - 67.55%) or (67.55% - 62%)
Margin of error = 5.55%
The margin of error for the given 95% confidence interval of the population proportion with limits (62%, 73.1%) is 5.55%.

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Answer:

The value of "x" is 5.

Step-by-step explanation:

In order to solve this system of equations, we first have to take the first equation and use it to represent "y" in terms of "x". We do that in the following way...

\(x + 3y = 2\\3y = 2 - x\\y = \frac{2}{3} - \frac{x}{3}\)

Now, we need to take the second equation and substitute "y" for the equivalent value in terms of "x". After doing this we will get the following equation, which we can solve to get the value of "x".

\(4x - 3y = 23\\4x-3(\frac{2}{3} - \frac{x}{3}) = 23\\4x - 2 + x = 23\\5x - 2= 23\\5x = 25\\x = 5\)

Therefore, the value of "x" is 5.

The value of "x" would be equal to 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given equation are;

x+3y = 2

4x−3y = 23

In order to solve this system of equations, we have to take the first equation and use it to represent "y" in terms of "x".

x+3y = 2

x = 2 -3y

Thus,

4x−3y = 23

4(2 -3y) −3y = 23

8 - 12y - 3y = 23

8 - 15y = 23

15y = -23 + 8

15y = - 15

y = -1

Now, we need to take the second equation and substitute "y" for the equivalent value in terms of x.

x+3y = 2

x= 2 - 3y

x = 2 + 3

x =5

Therefore, the value of "x" is 5.

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a. To select a committee of three men and four women, we can choose three men from six distinct men and four women from seven distinct women. This can be done in:

C(6, 3) * C(7, 4) = 20 * 35 = 700 ways.

Therefore, there are 700 ways to select a committee of three men and four women.

b. To select a committee of four persons that has at least one woman, we can either choose one woman and three men or choose two women and two men or choose three women and one man or choose four women. We can calculate the number of ways for each case and add them up to get the total number of ways.

One woman and three men: C(7, 1) * C(6, 3) = 7 * 20 = 140 ways

Two women and two men: C(7, 2) * C(6, 2) = 21 * 15 = 315 ways

Three women and one man: C(7, 3) * C(6, 1) = 35 * 6 = 210 ways

Four women: C(7, 4) = 35 ways

The total number of ways to select a committee of four persons that has at least one woman is the sum of the above cases:

140 + 315 + 210 + 35 = 700 ways.

Therefore, there are 700 ways to select a committee of four persons that has at least one woman.

c. To select a committee of four persons that has persons of both sexes, we can choose two men from six distinct men and two women from seven distinct women or choose three men from six distinct men and one woman from seven distinct women or choose one man from six distinct men and three women from seven distinct women. We can calculate the number of ways for each case and add them up to get the total number of ways.

Two men and two women: C(6, 2) * C(7, 2) = 15 * 21 = 315 ways

Three men and one woman: C(6, 3) * C(7, 1) = 20 * 7 = 140 ways

One man and three women: C(6, 1) * C(7, 3) = 6 * 35 = 210 ways

The total number of ways to select a committee of four persons that has persons of both sexes is the sum of the above cases:

315 + 140 + 210 = 665 ways.

Therefore, there are 665 ways to select a committee of four persons that has persons of both sexes.

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Answer: It will travel for 38.5 to 57.75 miles

Step-by-step explanation:

1) One gallon of gas will travel for at least 20-30 miles

Where 1155 miles will use 38.5 gallons or 58 gallons of gas

If its helpful please like thank you

a. The base calculation of the ticket price can be determined by considering various costs and factors associated with operating the bus. The calculation should include costs such as the initial price of the bus, fuel expenses, driver wages, insurance, maintenance, and other operational costs. By dividing the total costs by the number of passengers expected to be carried during the bus's lifespan, the base ticket price can be determined.

b. When suggesting the actual accumulated charges to be imposed in the future, it is important to consider factors such as inflation, changes in operating costs, market demand, and competitive pricing. The government should conduct market research and analysis to understand the dynamics of the transportation industry, evaluate the impact of potential charges on consumers and businesses, and strike a balance between affordability for passengers and profitability for bus operators. The suggested charges should aim to ensure sustainability and a fair return on investment for the operators, while also considering the economic well-being of the population.

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