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Answer:

(1) x=5 (2) I think the answer to 16 is 3/5 but not 100% sure

Step-by-step explanation:

(1) 29=5x+4

Step 1: Flip the equation.

5x+4=29

Step 2: Subtract 4 from both sides.

5x+4−4=29−4

5x=25

Step 3: Divide both sides by 5.

5x /5 =  25 /5

x=5

The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.

We need to calculate the percentage of the measurements contained in each of the following intervals:

According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).

Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).

Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).

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45^2=27^2+gh^2

2025=729+gh^2

2025-729=gh^2

1296=gh^2

underoot of 1296 =gh

36=gh

hope this helps you

Answer:

x= -5, 2

Step-by-step explanation:

set them equal to each other: \(x^{2}+5x-9=2x+1\)

subtract 2x from both sides: \(x^{2} +3x-9=1\)

subtract 1 from both sides to make it equal to zero: \(x^{2} +3x-10=0\)

find which 2 factors of -10 equal 3: 5 and -2

plug it into: \((x +?)\):  \((x+5) (x -2)\)

set both equations to zero: \(x +5=0\)         \(x-2=0\)

solve:  {x| x=-5, 2}

Answer:

24

Step-by-step explanation:

Option (a) is correct, i.e., the equation of the line in point-slope form with given slope -2/3 passing through the given point (2,-3) is y+3 = -2/3 (x-2).

Point slope form is used to represent a straight line using its slope and a point on the line.

The equation of a line in point-slope form whose slope is 'm' and which passes through a point (x₁ ,y₁) is

y - y₁ = m (x-x₁).

Here we have slope m= -2/3 and the point (x₁ ,y₁) = (2,-3).

Therefore, the point-slope form of the equation is

             y- (-3) = - 2/3 (x-2)

        ⇒ y + 3= -2/3 (x-2).

       ⇒ Option(a) is correct.

Therefore, equation of the line in point- form slope is y+3 = -2/3 (x-2).

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Answer:

x = 45

Step-by-step explanation:

Interior angles of a triangle sum up to 180

180 - 90 = 90

90 / 2 = 45

Answer:

X = 45

Step-by-step explanation:

Since all interior angles of a triangle add up to 180 and both of the missing angles are the same value, X would equal 45,

90+45+45=180

  Slope = 8 is the value of  equation of Slope Intercept Form .

What does the Slope Intercept Form Equation stand for?

A straight line's slope and the location of its y-axis intersection are utilized to determine the general equation of the line using the slope intercept equation. Y = mx + b is the slope intercept form equation. One formula for figuring out a line's equation is the slope-intercept formula. Y = mx + b is the slope-intercept formula for a line with slope m and y-intercept b. Any point on the line is (x, y) in this case.

Y= 8x + 5

Compare the equation to the y = mx + c

       slope = 8

             c = 5

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The value of each small coin(p) is 2.

The value of each large coin(p+5) is 7.

What is an equation?

Two expressions joined by an equal sign form a mathematical statement known as an equation.

It is given that the value of each small coin is denoted as 'p' and large coins worth extra 5 points.

then, the value of each large coin will be ' p+5 '

she collected 102 coins out of which 100 coins are collected as small coins, So the rest 2 coins will be large coins.

∴ Total points value = (value of each small coin × small coins) + (value of large coins × large coins)

                         214 = [p × 100] + [(p+5) × 2]

                         214 = 100p + 2p + 10

                         214 - 10 = 102p

                         204 = 102p

                         p = 204/102 = 2.

Hence, Value of each small coin is 2 and value of each large coin is 7 i.e. ( 2+5).

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Answer:

1.15 is 115%

Step-by-step explanation:

7/8 is 0.875 so it makes it 87.5%

The percentage form of the given number is:

1.15 as a percent is 115%

7/8 as a percent is 187.5%

To convert a decimal to a percent,

we need to multiply it by 100.

So for 1.15,

Multiply it by 100 to get 115%.

To convert a mixed number to a percent,

We have to convert it to an improper fraction first.

To do that, we multiply the denominator by the whole number and add the numerator.

Then we put that answer over the original denominator.

For 7/8, the improper fraction would be,

(8 x 1) + 7 = 15/8.

To convert this to a percentage,

We need to divide the numerator by the denominator and multiply by 100.

So 15/8 as a decimal is 1.875, and when we multiply that by 100 we get 187.5%.

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To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Step-by-step explanation:

a) If we let x be the measure of the smallest angle, then the measures of the other two angles are 2x + 10 and 2x, respectively. To find x, we need to use the fact that the sum of the angles in any triangle is 180 degrees.

So, we have:

x - 10 + 2x + 2x + 10 = 180

5x = 160

x = 32

Therefore, the measures of the angles are:

Smallest angle: 32

Middle angle: 2 * 32 + 10 = 74

Largest angle: 2 * 32 = 64

b) To determine the type of triangle, we need to compare the measures of its angles.

If all angles are less than 90 degrees, the triangle is an acute triangle.

If one angle is equal to 90 degrees, the triangle is a right triangle.

If one angle is greater than 90 degrees, the triangle is an obtuse triangle.

In this case, since none of the angles are equal to 90 degrees, the triangle is an acute triangle.

Answer:

N = 3

Step-by-step explanation:

\( \frac{28}{4} = \frac{21}{N} \\ \\ 28N = 21 \times 4 \\ 28N = 84 \\ \\ N = \frac{84}{28} \\ \\ N = 3\)

I hope I helped you^_^

Answer:

15 1/2

Step-by-step explanation:

Answer:

4/155

0.025 rounded to the nearest thousandth

Step-by-step explanation:

The graph of the relationship has an equation of m = 3.75k and it is is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The constant of proportionality is 3.75 grams/liter

This means that

k = 3.75

As a general rule

A proportional relationship is represented as

y = kx

In this case, we use

m = kv

Where

Using the above as a guide, we have the following:

m = 3.75k

So, the equation of the relationship is m = 3.75k

The graph of the relationship m = 3.75k is added as an attachment

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Rhian scored more in the Math test than in the English test because she had a higher percentage

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that: In the Maths test, Rhian scored 14 out of 17, hence:

Mark percentage = (14 / 17) * 100% = 82.35%

In the English test, Rhian scored 31 out of 39, hence:

Mark percentage = (31 / 39) * 100% = 79.49%

Rhian scored more in the Math test.

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Answer:

Step-by-step explanation:

Given that  : The average marks of candidates in an aptitude test was 128.5 with a standard deviation of 8.2. Three scores extracted from the test are; 148, 102 and 152.

The objective here is to determine the average of the extracted scores that are the extreme values (outliers)

NOW:

The average marks of candidates in an aptitude test was 128.5

i.e the Mean = 128.5

Standard Deviation = 8.2

outlier will be outsides;

then the range  will be    Mean  ± 3 × SD

= 128.5 ± 8.2 × 3

= 128.5 ± 24.6

Range is  ( 103.9  ,  153.1)

102 is outside this range

Hence, the average of the extracted scores that are extreme values (outliers) will be 102 only

Answer: that is a vertical angle

Step-by-step explanation:

whenever you see an odd shape like x it will always be vertical

Answer:

Negative

Step-by-step explanation:

It's negative because my math teacher said so a few years ago. Sorry for the not so great explanation... I didn't pay attention that day.

Answer:

x=3

Step-by-step explanation:

distribute 3 into (x+2)

3x+6=x+12

move all the x variables to one side and all the numbers to another side

3x+6=x+12                                                                                                                         -3x      -3x

6=-2x+12

-12       -12

6-12=-2x

-6=-2x

isolate x by dividing everything by -2

-6/-2=-2x/-2

eliminate the -2 multiplying the x with the -2 dividing the -2x

-6/-2= x

x=3

Answer:

x=3

Step-by-step explanation:

3(x+2)=x+12

First, distribute the 3(x+2).

3x+6=x+12

Next, subtract 1x from each side. That will cancel out the x in the x+12.

2x+6=12

Subtract 6 from both sides. Canceling out the 6 in the 3x+6.

2x=6

Divide both sides by 2.

x=3

The equation of a line is y = 14/4x - 30/4

The general formula for the equation of a line is expressed with;

y = mx + c

This is so, such that the parameters are given as;

From the information given, we have that;

Slope, m = y₂ - y₁/x₂ - x₁

Substitute the values, we have;

Slope, m = 24 - 10/9 - 5

subtract the values

Slope, m = 14/4

Substitute the value, we have;

10 = 14/4 (5) + c

multiply the values

c = 10 - 70/4 = 40 - 70 /4 = -30/4

The equation is;

y = 14/4x - 30/4

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A correlation coefficient (r) value of 0.98 indicates a strong, positive correlation between students' heights and their shoe sizes.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 1 represents a perfect positive correlation, and 0 represents no correlation.

In this case, a correlation coefficient of 0.98 indicates a strong, positive correlation between students' heights and their shoe sizes. The value being close to 1 suggests that there is a strong linear relationship between the two variables, and as one variable (height) increases, the other variable (shoe size) tends to increase as well.

The positive sign indicates that as heights increase, shoe sizes also tend to increase. This implies that there is a direct relationship between the two variables, and taller students generally have larger shoe sizes. Therefore, the correlation coefficient of 0.98 signifies a strong, positive correlation between students' heights and their shoe sizes.

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Answer:

1.Range = highest value - lowest value

R=552-225

R=327

2.Re-arrange the set of the data from ascending order

=234,355,470,476,765

Median is the middle value which is

=470

3. Mode is the most occuring frequency which is

=7

4. 1.Range = highest value - lowest value

R=99 - 43

R=56

5.No the range with not change because 76 is neither the highest nor the lowest value

Note: Range = highest value - lowest value

The probability of exactly 7 successful surgeries out of 11 is 0.168.

This problem can be solved using the binomial probability formula:

\(P(X = k) = C(n, k)\) ×\(p^k\) × \((1-p)^{n-k}\)

where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials (in this case, 11 surgeries)

k is the number of successful surgeries

p is the probability of success in a single trial (in this case, 0.4)

C(n, k) is the number of ways to choose k successes from n trials, which is calculated as n choose \(k = n! / (k!\)×\((n-k)!)\)

Using this formula, we can plug in the values and calculate the probability of getting exactly 7 successful surgeries:

\(P(X = 7) = C(11, 7)\) × \(0.4^7\)× \(0.6^{11-7}\)

\(= 330\) × \(0.0390625\) × \(0.279936\)

\(= 0.0968\) (rounded to four decimal places)

This situation can be modeled by a binomial distribution with n = 11 surgeries and p = 0.4 probability of success.

The probability of exactly k successes out of n trials is given by the binomial probability formula:

P(k successes) = (n choose k) × p^k × (1 - p)^(n - k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of exactly 7 successful surgeries out of 11 as follows:

\(P(7 successes) = (11 choose 7)\) × \(0.4^7\)× \(0.6^4\)

\(= (11! / (7!\) × \(4!))\) × \(0.4^7\) × \(0.6^4\)

\(= 330\) × \(0.004096\) × \(0.1296\)

\(= 0.168\)

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

The length of the common chord is 6 cm.

A line that touches ellipses or circles only once is said to be tangential.

Given:

Circles intersect at two points, so we can draw the above figure.

Let AB be the common chord.

Let O and O’ be the centers of the circles, respectively.

So, O’A = 5 cm, OA = 3 cm

OO’ = 4 cm

We can claim that the smaller circle's centre is inside the larger circle itself since the radius of the larger circle is greater than the separation between the two centres.

OO’ is the perpendicular bisector of AB.

So, OA = OB = 3 cm

AB = 3 cm + 3 cm = 6 cm [Since, O is the mid point of AB]

Hence, the length is 6 units.

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Answer:

Hope it will help U......

\( \large \tt \: m = - \frac{3}{7} \)

Answer:

slope = - \(\frac{3}{7}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, \(\frac{2}{7}\) ) and (x₂, y₂ ) = (1, \(\frac{5}{7}\) )

m = \(\frac{\frac{5}{7}-\frac{2}{7} }{1-2}\) = \(\frac{\frac{3}{7} }{-1}\) = - \(\frac{3}{7}\)