Two angles of a triangle measure 55° and 20°.
What is the measure of the third angle of the triangle?
A. 15°
B. 90°
C. 105°
D. 2850

Answer:

x=3

Step-by-step explanation:

First would need to convert the radical into a number.

And since if you have a perfect square of a radical it goes outside the square root sign, you would take the 3 and square it to make 9 and then take the 2 inside the square root sign and multiply so you have the square root of 18|

Since we have \(\sqrt{18}\) as the Leg c we would need to square it, squaring a square root sign would just cause them to be cancelled out and you being left with 18, afterwards find the square of 3, which is 9

18-9=9

square root of 9 = 3

True, The range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.


The range of a linear transformation defined by the matrix transformation t(x) = ax is equal to the column space of matrix A (col A).

The range of a linear transformation is the set of all possible output values. In this case, the matrix A represents the transformation, and the column space of matrix A represents the span of the columns of A. The column space of matrix A is the set of all possible linear combinations of the columns of A.

To prove that the range of the linear transformation t(x) = Ax is equal to the column space of matrix A, we can show that every vector in the column space of A can be obtained as an output of the transformation t(x) = Ax. Additionally, we can show that every output of the transformation t(x) = Ax belongs to the column space of A.


Therefore, it is true that the range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.

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The actual speck of dust is 0.24mm if a speck of dust in an electron microscope is 1.2 x 10² millimeters wide.

The ratio among comparable dimensions of an object and a model with that object, is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:

A speck of dust in an electron microscope is 1.2 x 10² millimeters wide.

Let d be the width of dust seen in electron microscope.

d = 1.2x10² mm

Let x be the scaling parameter.

x = 5x10²mm

D = d/x

D =  0.24mm

Thus, the actual speck of dust is 0.24mm if a speck of dust in an electron microscope is 1.2 x 10² millimeters wide.

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The distance traveled in the first 5.2 seconds when the speed dropped from the rest as v(t) = 9.8t is equal to 132.496 meters.

'v' is the speed of the object in meter per second

't' is the time in seconds.

Speed dropped from rest 'v(t) = 9.8t '

Distance traveled in the first 5.2 seconds is equal to

= \(\int_{0}^{5.2}\)9.8t dt

= ( 9.8 / 2 )t² \(|_{0}^{5.2}\)

Substitute the lower and upper limit to get the required distance we have,

= 4.9 [ ( 5.2)² - 0² ]

= 4.9 × 27.04

= 132.496 meters

Therefore, the distance traveled for the given first 5.2 seconds is equal to 132.496 meters.

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The above question is incomplete, the complete question is:

Free fall the speed v of an object dropped from rest is given by v(t)=9.8t where v is meters per second and time 't' is in seconds.

(a) Express the distance traveled in the first 5.2 seconds as an integral.

Answer:

yes is the 3rt answer

Step-by-step explanation:

Comolete question is;

One national survey found that 86 percent of those who were unhappily married but who stayed with the marriage were, when re-interviewed five years later,

A) preparing to divorce

B) resigned to the situation

C) mostly "very" or "quite" happy

D) mostly "very" happy

Answer:

C) mostly "very" or "quite" happy

Step-by-step explanation:

From social psychology, we know that;

Sometimes people could be happy about something but later on as things progress they become satisfied and are happy about that same thing or person.

The same is the case here with marriage and more importantly in this research.

It says they were unhappily married but they stayed in the marriage and were interviewed 5 years after that. Thus, for them to stay that long even after being unhappy, it means that they began to become a bit happy along the line.

Thus, they would gradually become happy or mostly happy.

Answer:

  3(x +2)

Step-by-step explanation:

If the number is represented by x, then "the sum of a number and 2" is ...

  x + 2

Three times that sum is ...

  3(x +2)

The height of the building from which the angle of elevation is 32 degrees is 127.87m.

The angle of elevation is found to be 32 degrees and when moving 50 closer to the building, the angle of elevation is 53.

Let us say that the height of the building is X.

Now, let us say the distance between the building and the person is Y.

So, we write,

tan(32°) = X/Y

Also, tan(53°) = X/(Y-50)

0.62 = X/Y and 1.32 = X/(Y-50)

0.62Y = 1.32Y - 66

66 = 0.32Y

Y = 206.25 m

Now, we know, X = 206.25m x 0.62

X = 127.87m

So, the height of the building is 127.87m.

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Scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

The evidence that allowed scientists to conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus comes from the application of the quantum mechanical model. The quantum mechanical model states that the energy of an electron is quantized, meaning it can only occupy discrete energy levels rather than any random energy level in between. This is expressed mathematically through the equation E n = nhf, which states that the energy of an electron is equal to the product of Plank's constant (h) and the frequency (f) of the electron's orbit multiplied by the quantum number (n). This equation demonstrates that electrons can only occupy certain energy levels and not any random energy level. Therefore, scientists can conclude that electrons occupy specific energy levels and are not just randomly distributed outside the nucleus.

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At a significance level of 5%, with a sample size of 800 items produced on a new machine and 48 of them being defective, the null hypothesis is that the proportion of defective items is not significantly more than 5%, while the alternative hypothesis is that it is significantly more than 5%. The level of significance is 0.05. Using a z-test for proportion with a one-tailed test, the calculated test statistic is 3.45. Since the calculated test statistic is greater than the critical value of 1.645, we reject the null hypothesis. Therefore, there is enough evidence to get rid of the machine.

Null Hypothesis: p = 0.05

Alternative Hypothesis: p > 0.05

Level of Significance: α = 0.05

Sample Size: n = 800

Number of Defective Items: x = 48

Sample Proportion:P= x/n = 48/800 = 0.06

Since the sample size is large, we can use the normal distribution to approximate the binomial distribution.

Test Statistic: z = (P - p) / sqrt(p * (1 - p) / n)

Under the null hypothesis, the test statistic follows a standard normal distribution.

Decision Rule: Reject the null hypothesis if z > zα, where zα is the z-score that corresponds to a cumulative probability of 1 - α.

From the standard normal distribution table, we have:

zα = 1.645

Computation:

z = (0.06 - 0.05) / sqrt(0.05 * 0.95 / 800) = 1.33

Since z (1.33) is less than zα (1.645), we fail to reject the null hypothesis.

Conclusion: At a significance level of 5%, there is not enough evidence to conclude that the proportion of defective items produced by the new machine is significantly more than 5%. Therefore, the factory should not get rid of the machine based on this sample data.

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Proportion is an expression that shows the relationship between two variables. Thus the proportion reasoning required is:

number of days = 1.5 * number of concerts

so that: x = 6.0 days

The relationship between two given variables can be expressed in the terms of proportion. These include direct proportion, inverse proportion, etc. When the proportional sign changes to equal to the sign, a constant of proportionality always exists.

Thus in the given question, it can be deduced that;

the number of days to set up is directly proportional to the number of concerts.

Such that;

number of days \(\alpha\) number of concerts

number of days = k * number of concerts

where k is the constant of proportionality.

number of days = 1.5 * number of concerts

So, when the number of concerts is 1, then the number of days required to set up is 1.5.

Thus, when the number of concerts is 4, then;

number of days = 1.5*4

                          = 6.0

Therefore the number of days to set up when there are 4 concerts is 6.0 days.

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The 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution is (0.022, 0.220)

The sample size of respondents with some college education is 325, and 133 of them believe in the theory of evolution. The sample size of respondents who were college graduates is 228, and 121 of them believe in the theory of evolution.

Now, the sample proportions are:p1= 133/325 = 0.410p2 = 121/228 = 0.531The point estimate of the difference in proportions is:p1 - p2 = 0.531 - 0.410 = 0.121

To calculate the standard error of the sampling distribution of the difference of two proportions, use the following formula:\($$SE = \sqrt{ \frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$\)

Substituting the values, we get,\($$SE = \sqrt{ \frac{0.410(1-0.410)}{325} + \frac{0.531(1-0.531)}{228}}$$\)

Solving the above expression, we get,\($$SE = 0.0489$$\)

Using the formula of the confidence interval,\($$\text{Confidence Interval} = \text{point estimate} ± \text{margin of error}$$\)

Substituting the values,\($$\text{Confidence Interval} = 0.121 ± 1.645 \times 0.0489$$\)

Now, solving the above expression, we get the confidence interval as:\($$(0.022, 0.220)$$\)

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The combination of  number of ways of groups of 3 customers are  19600 .

What is permutation and combination?

The number of store customer is N = 50

The number of customer that receive a special gift is r = 3

The expression for the number of possible ways to choose 3 customers is

                   = ⁿCr

                   = ⁵⁰C₃

                    = 50 * 49 * 48/3 * 2 * 1

                    = 19600

Thus, the number of ways of groups of 3 customers are  19600.

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a) The equation 1 has an infinite number of solutions, as both linear functions have the same slope and internet, hence Nyoko is incorrect.

b) Nyoko cannot find a value of b so that the equation has no solutions.

The equation 1 is given as follows:

6x - 5 + 2x = 4(2x - 1) - 1.

Combining the like terms and applying the distributive property, the simplified equations are given as follows:

8x - 5 = 8x - 4 - 1

8x - 5 = 8x - 5.

As they are linear functions with the same slope and intercept, the number of soltuions is of infinity.

The equation 2 is given as follows:

3x + 7 = bx + 7.

A system of linear equations will have zero solutions when:

As they have the same intercept for this problem, it is not possible to attribute a value of b such that the equation will have no solution.

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(a) The domain closed and bounded.

(b) The domain bounded.

(c) The domain closed.

(d) The domain bounded.

(e) The domain closed and bounded.

(f) The domain closed and bounded.

In this question, we have been given some domains.

We need to check which domains are closed and which are bounded.

A domain of function is said to be closed if the region R contains all boundary points.

A bounded domain is nothing but a domain which is a bounded set.

(a) {(x,y)∈R2:x^2+y^2≤1}

The domain of x^2+y^2≤1 contains set of all points (x, y) ∈R2

so, the domain closed and bounded.

(b) {(x,y)∈R2:x2+y2<1}

The domain of x^2+y^2 < 1 contains set of all points (x, y) ∈R2

so, the domain is bounded.

(c) {(x,y)∈R2: x ≥ 0}

The domain of x ≥ 0 is R2 - {x < 0}

So, the domain is closed.

(d) {(x, y) ∈ R2 : x > 0,y > 0}

The domain is R2 - {(x, y) ≥ 0}

So, the domain is bounded.

(e) {(x, y) ∈ R2 : 1 ≤ x ≤ 4, 5 ≤ y ≤ 10}

The domain is closed and bounded.

(f) {(x,y)∈R2:x>0,x^2+y^2≤10}

The domain is closed and bounded.

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Answer:

We know that P(x) = 30*x^3 + k*x^2 + 1

a) If (3x - 1) is a factor, let's find the value of k.

Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.

Then:

30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)

30*x^3 + k*x^2 + 1  = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c

30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c

The terms with the same exponent should be equal, then:

30*x^3 = 3*a*x^3

30 = 3*a

30/3 = a = 10

k*x^2 = (3*b - a)*x^2

k = (3*b - 10)  

0*x = (3*c - b)*x

0 = (3*c - b)

b = 3*c

and

1 = -c

then:

c = -1

Replacing this in the equation: b = 3*c

we get: b = -3

Replacing this in the equation for k, we get:

k = (3*b - 10) = (3*-3 - 10) = -19

k = -19

And we can write:

P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)

b) Now we want to write P(x) as a product of its linear factors.

Then we need to factorize the quadratic part:

We need to solve

10*x^2 - 3*x - 1 = 0

We can use the Bhaskara's equation to get the solutions:

\(x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}\)

Then the two zeros of that polynomial are

x = (3 + 7)/10 = 1

x = (3 - 7)/10 = - 4/10 = -2/5

So we can write the polynomial as:

10*(x - 1)*(x - (-2/5))

Replacing this in the equation of P(x) we get:

P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)

     = 10* (3*x - 1)*(x -1)*(x + 2/5)

So P(x) is written as a product of lineal factors.

C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.

For the first factor, we have a zero at x = 1/3

for the second, we have a zero at x = 1

for the third one, we have a zero at  x = -2/5

Answer:

f(x) = 25,000 ( 1 + 0.025 )ˣ

Step-by-step explanation:

Given word problem becomes

f(x) = 25,000 ( 1 + 0.025 )ˣ

Answer:

294 cm^2

Step-by-step explanation:

length of the cube is 7cm each side

S.A = 2(7 * 7) + 2( 7 * 7) + 2( 7 * 7)

= 294 cm^2

Answer:

5^5+4/5^6

5^9/5^6

5^9-6

5^3

125

Step-by-step explanation:

Firstly the powers of 4 adds up

Then net power is formed by (9-6) ie 3

Lastly 5^3 is result which is 125

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The degree measure of each angle in the triangle is

∠H = 59°

∠F = 39°

Angle sum property of triangle says that sum of all the triangle is always equal to 180°

∠G is given to us as 90°

So by applying the property we an say that

90 + (3x - 14) + (5x - 16) = 180

8x = 180 - 90 + 14 + 16

8x = 120

x = 15

∠H =  5x - 16

∠H = 5*15 - 16

∠H = 75 - 16

∠H = 59°

∠F = 3x - 14

∠F = 3*15 - 14

∠F = 45 - 14

∠F = 39°

Therefore ∠H = 59° and ∠F = 39°

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Answer:

3-3x/8

Step-by-step explanation:

Answer:

I believe it's option C

Step-by-step explanation:

A function is a relation that does not contain two pairs with same first component.

option C

{(-1,2),(3,-2),(0,1),(3,5)} is not a function, since there are two pairs with the same first component i.e, 3

hope it helps

mark me brainliest pls

Answer:

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

Step-by-step explanation:

The surface are of rectangular prism = 140 ft²

Surface area of rectangular prism is given by :

A = 2(lw + lh + wh)

Using trial by error method :

6 feet by 2 feet by 3 feet

A = 2(6*2 + 6*3 + 2*3) = 72ft²

6 feet by 5 feet by 4 feet

A = 2(6*5 + 6*4 + 5*4) = 148 ft²

7 feet by 6 feet by 4 feet

A = 2(7*6 + 7*4 + 6*4) = 188ft²

8 feet by 4 feet by 3 feet

A = 2(8*4 + 8*3 + 4*3) = 136ft²

The correct statement that assigns the value 1.667 to the array "fractions" at element 9 is not included in the options given.

It is important to note that arrays start counting from 0, so the 9th element would be at index 8. If there was a statement like "fractions[8] = 1.667", then that would be the correct answer.

However, since none of the options include the correct index, none of them are assigning the value 1.667 to the 9th element of the "fractions" array.

None of the options have the index of 9, and therefore cannot assign a value to that specific element

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Answer:

2.22

Step-by-step explanation:

\(\sqrt[3]{11} =2.223980091\)

Rounded to hundredths: 2.22

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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Answer:

18

Step-by-step explanation:

168 : 28 : : 108 : y

168 / 28 = 108 / y

6 = 108 / y

6 * y = 108

y = 108 / 6

y = 18

Answer:

y = 18

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 28 when x = 168

28 = 168k ( divide both sides by 168 )

\(\frac{28}{168}\) = k , that is

k = \(\frac{1}{6}\)

y = \(\frac{1}{6}\) x ← equation of variation

When x = 108 , then

y = \(\frac{1}{6}\) × 108 = 18