solve the inequality 5x + 3 ≥ 48

Answer:

mAngle B =70°

Step-by-step explanation:

The question says to find the "measure of Angle B"

The triangle there is an isosceles triangle. That means two of the sides are the same size. The angles opposite from those equal sides are also equal.

BA = BC = 40cm

So Angle A = Angle C = 55°

All three angles in a triangle add up to 180°

55 + 55 + B = 180

110 + B = 180

B = 70°

The measure of angle B is 70°

The missing lengths of the sides  a = 3 inches  , b =  3√3 inches  .

90 -60 -30 triangle .

We have given 90 -60 -30 triangle with hypotenuses = 6 in.

By the 90 -60 -30 triangle rule  :  The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle and the length of the longer leg is 3√ times the length of the shorter leg.

Then Shorter leg = a longer leg = b.

Hypotenuse = 2 * Shorter leg .

Plug the values.

6 =  2 *  Shorter leg .

On dividing both sides by 2

Shorter leg (a)  = 3 inches .

Then by the rule :  longer leg is 3√ times the length of the shorter leg.

Longer leg =  3√Shorter .

Longer leg (b)  =  3√3 inches  .

Therefore, a = 3 inches  , b =  3√3 inches  .

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SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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Answer:

3x + 12 + x = 180

4x +12 = 180

4x = 168

x = 42

(I'm guessing you're in a different timezone than I am because it's already 3:35 here)

The directional derivative of z = 3x^4 - xy + y^3 at the point M = (1,2) in the direction that forms a 60 degree angle with the x-axis is 5 + 17sqrt(3)/2.

The directional derivative of z = 3x^4 - xy + y^3 at the point M = (1,2) in the direction that forms a 60 degree angle with the x-axis is given by:

D_v(z) = grad(z) . v

where v is the unit vector in the direction of interest. To find v, we can use the fact that it makes a 60 degree angle with the x-axis, so its components are (cos(60), sin(60)) = (1/2, sqrt(3)/2).

The gradient of z is:

grad(z) = <∂z/∂x, ∂z/∂y> = <12x^3 - y, -x + 3y^2>

So at the point M = (1,2), we have:

grad(z) = <12(1)^3 - 2, -1 + 3(2)^2> = <10, 17>

Now we need to compute the dot product of grad(z) and v:

grad(z) . v = <10, 17> . <1/2, sqrt(3)/2> = 10/2 + 17(sqrt(3)/2) = 5 + 17sqrt(3)/2

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The probability of selecting a driver who prefers one of these brands is:12/50 + 8/50 + 6/50 + 24/50 = 0.5 or 50%.Therefore, the answer is 0.5 or 50%.

a) How likely is it that a randomly selected motorist would choose PUMA? The frequency distribution of the gasoline brand that is most preferred by a sample of fifty motorists in Windhoek is shown in the table below: Brand of gas NAMCOR128PUMA66SHELL24ENG8a) The probability that a randomly selected driver would choose PUMA is 6/50, which can also be written as 0.12 or 12 percent.

Accordingly, the response is: The probability that a randomly selected motorist does not prefer NAMCOR is the same as 1 minus the probability that they do prefer NAMCOR.12 out of 50 drivers prefer NAMCOR, which is 24% or 0.24. Therefore, the probability that a randomly selected motorist does not prefer NAMCOR is 1 - 0.24 = 0.76 or 76%. Therefore, the answer is 0.76 or 76%.c) The probability that a motorist in the selected sample prefers either NAMCOR, ENGEN, PU Brand of gas NAMCOR128PUMA66SHELL24ENG8

The probability of selecting a driver who prefers NAMCOR, ENGEN, PUMA, or SHELL can be calculated by adding their respective probabilities. The probability of selecting a driver who prefers one of these brands is, as a result, 12/50, 8/50, 6/50, and 24/50, or 50%. Accordingly, the response is 0.5, or 50%.

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Answer:

C. The hypotenuse is \(\sqrt{2}\) times as long as either leg.

Step-by-step explanation:

The hypotenuse is square root 2 times as long as the sides is a true statement.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the true statement about an isosceles right triangle.

Let us use pythagoras theorem to find this

h²=a²+b²

In this case since its an isosceles right triangle, a and b most be the same.

Let's say that the measure of the sides that are equal is x and the hypotenuse is h.

Pythagoras tells us the following:

h²=x²+x²

h²=2x²

Take square root on both sides

h=√2x

Hence, the hypotenuse is square root 2 times as long as the sides

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No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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The number of students that voted is given as follows:

5 students.

The number of students that voted is obtained applying the proportions in the context of this problem, multiplying the total number of students by the decimal equivalent of the percentage.

The total number of students is given as follows:

20 students.

The decimal equivalent of the percentage is given as follows:

25/100 = 0.25.

Hence the number of students that voted is given as follows:

0.25 x 20 = 20/4 = 5 students.

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Answer:

Step-by-step explanation:

104 units

The region graph enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows.

1. Plot the graphs of the given functions:

y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3.

2. Shade the area enclosed the two graphs.

3. The region enclosed by the given functions is shown below.

The region enclosed by the given functions y = sec2(x) and y = 8 cos(x) for -3 ≤ x ≤ 3 can be sketched as follows. Firstly, plot the graphs of the two functions on the same coordinate plane. Then, shade the area enclosed by the two graphs. The resulting region is a curved area that starts from the point (-3, 8 cos(-3)) on the left, curves up until it reaches the point (3, 8 cos(3)) on the right and then curves down until it reaches the point (-3, 8 cos(-3)). The enclosed region is a continuous, curved area that lies between the two graphs.

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The correct answer is "line of best fit." A regression line is also called the line of best fit as it represents the best approximation of the relationship between the independent and dependent variables in a scatterplot.

In statistics and data analysis, a regression line is a straight line that represents the best-fitting relationship between two variables. It is often referred to as the "line of best fit" because it minimizes the overall distance between the line and the actual data points.

When plotting data points on a scatterplot, the regression line is used to approximate the trend or pattern in the data. It helps in understanding the relationship between the independent variable (usually denoted as "x") and the dependent variable (usually denoted as "y"). The goal is to find a line that is as close as possible to all the data points, capturing the general trend or direction of the relationship.

The line of best fit is determined by using a statistical technique called regression analysis. This technique calculates the optimal values for the slope and intercept of the line based on the data. The most common method for fitting a regression line is known as ordinary least squares (OLS), which minimizes the sum of the squared differences between the observed data points and the predicted values on the line.

By fitting a regression line, we can make predictions or estimations about the dependent variable based on the values of the independent variable. The line of best fit provides a visual representation of the relationship between the variables and allows for easier interpretation and analysis of the data.

It's important to note that the line of best fit is an estimation based on the given data, and it may not perfectly pass through every data point. However, it provides a useful summary of the overall trend and can be used for making predictions or drawing conclusions about the relationship between the variables.

Therefore, the correct answer is "line of best fit." A regression line is also called the line of best fit as it represents the best approximation of the relationship between the independent and dependent variables in a scatterplot.

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Answer:

⏬⬇⤵

Step-by-step explanation:

The Fundamental Theorem of Algebra states that the degree of a polynomial is the maximum number of roots the polynomial has. A third-degree equation has, at most, three roots.

So:

1. 3

2. 4

3. 3

4. 0

5. 1

6. 4

Answer:

Earthquakes

Step-by-step explanation:

Earthquakes are vibrations of the earth’s crust caused by movement at plate boundaries and major fault lines.

The conditions for conducting one-sample t-procedures are as follows:

1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.

2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.

3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.

4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.

5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.

It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.

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Answer:

Loading,please wait...

Step-by-step explanation:

The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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If A(3,-4) and B(13,11), the coordinates of the point 3/5 from A to B is, (9, 5).

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Section formula for a point which divides line joining points into m:n ratio,

(X,Y) = { (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n }

Given that, two points,

A(3, -4) and B(13, 11),

the coordinates of the point 3/5 from A to B

Difference, in x coordinates

13 - 3 = 10

It is 3/5 from A to B

So,    x coordinate is,3 + 10 × 3/5 = 9

Difference, in y coordinates

11 -(-4) = 15

It is 3/5 from A to B

So,    y coordinate is, -4 + 15 × 3/5 = 5

Hence, the point is (9, 5)

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Check the picture below.

so we only want the area in pink.

\(\stackrel{\textit{left and right}}{2(4)(11)}~~ + ~~\stackrel{\textit{front and back}}{2(4)(11)}\implies \text{\LARGE 176}~cm^2\)

Answer: 0.35x + 12.00 = 14.35

Explanation: You would make sure to include the x since we are unsure of how many apples to bought, we know the total it will be at the other side of the equal sign, she spent 12 on her groceries so we would add that to the number of apples she got.

Given:

Principal Amount, P = $4,400

Interest rate, r = 90%

Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.

This is a Compound interest problem.

To find create an exponential equation, apply the formula below:

WHere:

P is the principal amount = $4,400

r is the rate = 90% = 0.90

t is the time (number of years)

Input values into the equation above:

Therefore, the exponential equation that allows her to track the interest earned over time is:

Plugging the value for the number of years for t, you will get the interest earned over time, t.

ANSWRER:

Answer:

31. (25 - 8) x 3 = 51

32.  9 + 4 x (5 - 3) = 17

Step-by-step explanation:

grouping symbols

31.) 25 - 8 x 3 = 51

(25 - 8) x 3 = 51

Do the parentheses first

17 * 3 = 51

51=51

32.) 9 + 4 x 5 - 3 = 17

9 + 4 x (5 - 3) = 17

Parentheses first

9 + 4 * 2 = 17

Multiply

9+8 = 17

Add

17=17

Answer:

y = 3

Step-by-step explanation:

All this question is asking is:

When x = 1, what does y equal?

To solve this problem, plug in 1 for x to get

\(y = \frac{1}{2} *6^1\)

Then, simplify!

Any number to the first power is the same number, so \(6^1 = 6\).

\(\frac{1}{2} * 6 = \frac{6}{2} = 3\)

y = 3.

Hope this helps!

The answer should be .7

Answer:

0.7

Step-by-step explanation:

Step 1:

21÷30= 7÷10

Step 2:

7÷10= 0.7

Answer:

is there a picture

Step-by-step explanation:

Point (4,0) and (0,7) (C) were passed through by the line equation of 7x1 + 4x2 = 28.

From the case, we know that:

Line equation: 7x1 + 4x2 = 28

Passed through points?

To answer this question, we can try to find some conditions:

First, we will try to find the valuf f x2 if x1 = 0:

(x1 = 0)

7(0) + 4.x2 = 28

0 + 4.x2 = 28

4.x2 = 28

x2 = 7 --> (0,7)

Next, we try if x2=0, then x1 = ...

(x2 = 0)

7x1 + 4(0) = 28

7x1 = 28

x1 = 4 --> (4,0)

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Answer:

.

Step-by-step explanation:

.