pa
Use AABC for questions 2 and 3.
B
12
15
6 a
A
C
2. State the three basic trigonometric ratios for LB.
3. Find a (to the nearest tenth of a degree).

a) For equation y = x

x and y are directly proportional and the constant of proportionality k = 1

b) For equation y = -52x

x and y are directly proportional and the constant of proportionality k is -52

A) Consider equation y = x

For x = 1, y = 1

For x = -1, y = -1

And for x = 1/2 the value of y is 1/2

This means that y is directly proportional to x.

And the  constant of proportionality k would be,

k = y/x

k = 1

B) Consider equation y = -52x

For x = 1 the value of y is -52

For x = -1,  the value of y is y = 52

And for x = 0 the value of y is 0

This means that y is directly proportional to x.

And the  constant of proportionality k would be,

k = y/x

k = -52

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Check the picture below.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$225\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 225[1+(0.06)(5)]\implies A=225(1.3) \implies A = 292.5[/tex]

The probability that a resident who has only completed high school are aged 30-39 = 0.059

We know that the probability of event A is given by the formula,

P(A) = number of possible outcomes of event A / total number of outcomes

We need to find the probability that a resident who has only completed high school are aged 30-39.

Let event A: a resident who has only completed high school are aged 30-39.

The number of  resident who completed high school and aged 30-39 = 933

And the total nuember of residnts = 15818

Using probability formula the required probability would be,

P(A) = n(A)/n(S)

P(A) = 933/15818

P(A) = 0.059

This is the required probability.

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Find the complete question below.

The equation of the function y = -2(1.03)^x  is a growth function i.e. A Growth 3%

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

y = -2(1.03)^x

An exponential function is represented as

y = ab^x

If b > 0, then it is a growth function

Otherwise, it a decay function

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

y = -2(1.03)^x  -- growth

This also means that the rate of growth is 3%

Hence, the function y = -2(1.03)^x  is a growth function

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The calculated value of the solution to the system of equations  (- 1, - 1)

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

The graph

The solution to the system of equations is the point of intersection between the lines on the graph

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

Intersection point =  (- 1, - 1)

This means that the solution to the system of equations  (- 1, - 1)

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The ratios as a fractions without reducing are:

a. 6/13

b. 7/40

c. 45/36

d. 37/43

To express a ratio as a fraction, we simply write the first number (the antecedent) as the numerator and the second number (the consequent) as the denominator. We do not reduce the fraction to its lowest terms because it changes the value of the ratio. For example, the ratio 6:13 cannot be reduced to 3:7 because they are not equal.

By expressing the ratios as fractions, we can easily compare and calculate with them, especially in mathematical operations such as multiplication and division. It is also a common practice in statistics to represent ratios as fractions, which can be useful in interpreting data and making comparisons between groups.

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Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

An equation that shows how to find the pounds of seed, p, needed for h hectares of land is p = 20h.

An equation that shows how many hectares, h, Harper can plant with p pounds of seed is h = p/20.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this table;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (300 - 200)/(15 - 10)

Slope (m) = 100/5

Slope (m) = 20

At data point (10, 200) and a slope of 20, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 200 = 20(x - 10)  

y = 20x - 200 + 200

y = 20x ≡ p = 20h

Making h the subject of formula, we have:

h = p/20

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Let x be mr sanchez
Let y be mr kelly

1.45x + 1.25y = 70.85
x + y = 53

x = 53 - y

1.45(53 - y) + 1.25y = 70.85
y = 30

sanchez sold 23 while kelly sold 30
sanchez: 1.45(23) = $33.35

kelly: 1.25(30) = $37.5

therefore kelly earned more
kelly earned $4.15 dollars more (37.5-33.35)

The slope of this line is equal to 3/5.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points (0, 0) and (5, 3) into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3 - 0)/(5 - 0)

Slope (m) = 3/5.

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The inequality that represents the values of x is expressed as:

7/4 < x < 11/2.

According to the triangle inequality theorem, any two sides of a triangle, when added, must be greater than the length of the third side.

Therefore, applying the triangle inequality theorem, we have:

2x + 4 + 6x > 18

8x + 4 > 18

8x > 18 - 4

8x > 14

x > 14/8

x > 7/4 or 7/4 < x

Therefore, the possible value of x would be: 7/4 < x < 11/2

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Answer:

the value of the expression 14 1/3 - 6 5/8 is 185/24.

Step-by-step explanation:

To solve this problem, you can convert both mixed numbers to improper fractions, then subtract the fractions and simplify the result. Here are the steps:

1. Convert 14 1/3 to an improper fraction:

14 1/3 = (14 x 3 + 1) / 3 = 43 / 3

2. Convert 6 5/8 to an improper fraction:

6 5/8 = (6 x 8 + 5) / 8 = 53 / 8

3. Subtract the fractions:

43 / 3 - 53 / 8 = (43 x 8 - 53 x 3) / (3 x 8) = (344 - 159) / 24 = 185 / 24

So the value of the expression 14 1/3 - 6 5/8 is 185/24.

Step-by-step explanation:

1. Anova analysis shows that the P-value is 0.2762. This is greater than the significance level of 0.05. This means that there is no statistically significant difference in the popularity of the desserts.

2. F-stats  ( 1.4038 )         P-value ( 0.2762)    DF ( 2  and 15)

3. The critical F-value at 95% is 3.68. It means that it is not statistically significant at at 95% level.

The critical F-value is a value used in hypothesis testing, specifically in ANOVA (Analysis of Variance).

It is defined by the test's degrees of freedom and the specified significance level (typically written by, such as 0.05 for a 95% confidence level).

            For the table provided, below is the ANOVA analysis.

                               Data summary from ANOVA analysis

Groups       N            Mean           Std Deviation             Std. Error

Pies             5             4.2                  1.9235                      0.8602

Cakes          6           4.8333               2.7869                    1.1377

Cookies       7            6.2857               1.8898                   0.7143

    Source                 DF           SS             MS           F-stats           P-value

Between groups       2        14.049       7.0246          1.4038           0.2762

Within groups           15          75.0615      5.0041

Total                          17             89.1107

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Answer:

None is obtuse

Step-by-step explanation:

An obtuse is something more than 180°and less than 360°

A.35°+65°+80°=180° Not obtuse

B.30°+40°+110°=180° Not obtuse

60°+60°+60°=180° Not obtuse

C.30°+60°+90°=180° Not obtuse

Answer:

B. a triangle with angles that measure 30°, 40°, and 110°

Step-by-step explanation:

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Note that the area of the shaded region is 0.4129. See how it was derived.

Using the standard normal distribution table, the area to the left of

z = 0.22 is 0.5871.

Therefore,  the area of the shaded region to the right of z = 0.22 is

1 - 0.5871 = 0.4129

  Rounding to 4 decimal places, the area of the shaded region is 0.4129.

The shaded region's area is the difference between the area of the complete polygon and the area of the polygon's unshaded portion.

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The probability of picking a 7 and then picking a number greater than 7 is 1/3.

Now, given that we have already picked three cards. So, 7, 8, and 9.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

The number of possible outcomes is 3.

Probability of picking 7 = 1/3

Now, as card seven is already picked up cards 8 and 9 are the only card left.

therefore, the sample size(possible outcomes) was reduced to 2 only.

Also, cards 8 and 9 both are greater than 7, thus the desired outcome is also 2.

Further the probability of the number greater than 7 occurring,

Probability (n>7) = 2/2 =1

Probability picking a number greater than 7

The probability of picking a 7 and then picking a number greater than 7

= Probability of card 7 occuring x probability of card 8 and 9 occurring

= 1/3 ×1

= 1/3

Hence, the probability of picking a 7 and then picking a number greater than 7 is 1/3.

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"Your question is incomplete, probably the complete question/missing part is:"

You pick a card at random. Without putting the first card back, you pick a second card at random. There're 3 cards. One is 7, one is 8, and the other is a nine. What is the probability of picking a 7 and then picking a number greater than 7? (Write the probability as a fraction or whole number.)

Answer: 4224.413805 miles

Step-by-step explanation:

First, we use The Pythagorean Theorem equation to find the distance between California and Florida

Equation: [tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]

[tex]3186^{2}[/tex]+[tex]2774^{2}[/tex]=[tex]c^{2}[/tex]

So, we are trying to solve for c.

The first thing we do is evaluate the expression.

10,150,596+7,695,076=[tex]c^{2}[/tex]

Add like terms

17,845,672=[tex]c^{2}[/tex]

Then, do inverse operations and square root 17,845,672

You would then get 4224.413805 miles.

The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

t = 9.79 years

Given that;

The number of miles m (in billions) traveled by vehicles in City A can be modeled by,

m = 2.86t + 112

where t is the number of years since 1994.

Hence, We can formulate;

The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

m = 2.86t + 112

140 = 2.86t + 112

140 - 112 = 2.86t

28 = 2.86t

t = 28/2.86

t = 9.79 years

Thus, The value of the year in which the number of vehicle miles of travel in City A was 140 billion is,

t = 9.79 years

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The calculated value of the weight in kilograms is 60 kg

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

He stepped on a scale and he weighed 132 pounds

This means that

Weight = 132 pounds

By the metric units of conversion, we have

1 pound = 0.453592 kg

Substitute the known values in the above equation, so, we have the following representation

Weight = 132 * 0.453592 kg

Evaluate

Weight = 59.87 kg

Approximate

Weight = 60 kg

Hence, the weight is 60 kg

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The expression that is equivalent to given expression (2x+8)(5x-7) is 10x² + 26x - 56.

To find the equivalent expression of (2x+8)(5x-7), we need to use the distributive property of multiplication.

First, we distribute 2x to both terms inside the second parentheses, and then we distribute 8 to both terms inside the second parentheses. This gives us:

(2x)(5x) + (2x)(-7) + (8)(5x) + (8)(-7)

Simplifying the terms inside each set of parentheses, we get:

10x² - 14x + 40x - 56

Combining like terms, we have:

10x² + 26x - 56

The distributive property of multiplication is a fundamental property in mathematics that helps simplify expressions by breaking down a term into smaller, more manageable parts.

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Answer:

15/10 = 32 = 1 12 = 1.5

Step-by-step explanation:

brainiest would be most needed thx

Answer: C (28)

Step-by-step explanation:

Use probabilities:

24/18 = x/21

Cross multiply: 18x=24*21

18x = 504

x=28

Step-by-step explanation:

to[tex]3w - 7 = \sqrt{8w - 7} \\ {(3w - 7)}^{2} = ({ \sqrt{8w - 7} })^{2} \\ 9 {w}^{2} - 42w + 49 = 8w - 7 \\ 9 { w}^{2} - 42w - 8w + 49 + 7 = 0 \\ 9 {w}^{2} - 50w + 56 = 0 \\ (9w - 14)(w - 4) = 0 \\ w = \frac{14}{9} \: or \: w = 4[/tex]

to make sure the answer

substitute w = 14/9 and w = 4 to the equation.

if w = 14/9

[tex]3w - 7 = \sqrt{8 w - 7} \\ 3 \times \frac{14}{9} - 7 = \sqrt{8 \times \frac{14}{9} - 7} \\ - \frac{ 7}{3} = \frac{7}{3} [/tex]

we know that if we substitute w = 14/9, the answer is not the same.

if w = 4

[tex]3w - 7 = \sqrt{ 8 w - 7 } \\ 3 \times 4 - 7 = \sqrt{8 \times 4 - 7} \\ 5 = 5[/tex]

if we substitute w = 4 the answer is the same.. we can conclude the the answer of 3w - 7 = √8w - 4 is 4

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{b}\\ a=\stackrel{adjacent}{3}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ b=\sqrt{ 3^2 + 3^2}\implies b=\sqrt{ 9 + 9 } \implies b=\sqrt{ 18 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{7}\\ a=\stackrel{adjacent}{\sqrt{18}}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 7^2 - (\sqrt{18})^2}\implies h=\sqrt{ 49 - 18 } \implies h=\sqrt{ 31 }\implies h\approx 6[/tex]

Answer:

6 ft

Step-by-step explanation:

In the right triangle ABC connect points A and B

BC=3ft

AC=3ft

AB² =BC² + AC²=9+9=18ft²

In the right triangle ABD, AB²=18ft

BD=7ft

AB²+AD²=BD²

18+AD²=7²

AD²= 49-18

AD=[tex]\sqrt{31\\[/tex]    =5.6

the length of AD is a whole number, round it

AD=6ft {the shortest height}

The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

h=4

Explanation:

Area of a parallelogram can be calculated by using the formulae :

A=bh ,

where A = Area, b = Base Length and h = Height

Therefore, by using the given information,

∴ 24 = 6h

∴ h=4c

Answer:

9.35

Step-by-step explanation:

P=SxSxS

=3.2+4.25+2.8

=9.35

10√15 + 2 is a simplified expression of the given expression.

We need to use the distributive property of multiplication to simplify the expression:

√6(5)√10 + 2

= 5√6√10 + 2

Since √6 and √10 cannot be simplified any further, we can multiply them together to get:

√6√10 = √(6 × 10) = √60

Now, we need to simplify the expression using this result:

5√6√10 + 2

= 5(√60) + 2

= 5(√4 × √15) + 2

= 5(2√15) + 2

= 10√15 + 2

Therefore, √6(5)√10+2 simplifies to 10√15 + 2.

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From the figure, the values of |BC| = 13cm,|AC| = 17cm,  |DB| = 36cm, |DC|= 8cm, |DE| = 24cm, |EC| = 18 cm, |EA| = 21cm

The sine rule, also known as the law of sines, is a relationship that states that side “a” divided by the sine “a” is equal to side “b” divided by the sine “b”. It can be used to find unknown lengths or angles of a triangle and its formula can be written as Sin A/a

The sine rule states that

a/sinA = b/sinB = c/sinC

To find the value of |BC| using the above formula.

a/sin41 = 20/sin78

a= (20/sin78 ÷sin41)

a = 20* 0.6561 /0.9782

a = 13cm

/BC/ = 13cm

To find |AC| using the same formula

a/sinA = b/sinB = c/sinC

note that <A = 180 - (78+41) = 61

b/sin61 = 13/sin41

b = (13*sin61)/sin41

b = 13* 0.8746/0.6561

b = 17cm

/AC/ = 17cm

To find /DB/ using the same formula

a/sinA = b/sinB = c/sinC

Note that <DCB = 180 - (60+31)  = 180-91 = 89

c/sin89 = 31/sin60

c = 31 / 0.8660 ÷ 0.9998

c = 36cm

/DB/ = 36cm

To find /DC/ using the same formula

a/sinA = b/sinB = c/sinC

b/sin31 = 13/sin60

b = 13*sin60)/sin31

b = 13*0.5150 /0.8660

b = 7.7cm

|DC| = 8cm

To find /ED/ using the same formula

a/sinA = b/sinB = c/sinC

Note that <DCE = 180- (36+15) = 129

Tis implies that

c/sin129 = 8/sin15

c= (8*0.7771)/0.2588

c = 24 cm

To find |EC| using the same formula

a/sinA = b/sinB = c/sinC

d/sin36 = 8/sin15

d*sin15 = 8*sin36

d= (8*sin36)/sin15

d = (8*0.5878)/ 0.2588

d = 18cm

|EC|= 18 cm

Finally, To find |EA| using the cosine  formula

Note that < ECA = 180-78 = 102

c² = a² +e²-2*aecos102

c²= 18²+8²-2*18*8*-0.2079

c² = 324 +64 +60

c² = 448

c √448

c = 21cm

|EA| = 21cm

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