1. Solve for the missing sides of the right triangle. Round to the nearest hundredth. 29 50° ​

Answer:

67p + 35

Step-by-step explanation:

Reduce all the unnecessary plus and minus signs. A plus and negative sign equates to just a minus sign.

4p + -7(-5 + -9p) = 4p - 7(-5 - 9p)

Expand the variables in the brackets. These take priority over regular evaluation of the other signs. Two negative values multiplied together produces a positive product.

4p - 7(-5 - 9p) = 4p + 35 + 63p

Add all like products together.

4p + 35 + 63p = 67p + 35

Check that the final simplification can no longer be simplified.

129 students had a private scholarship.

Out of the 843 students,

To calculate the total number of students with a private scholarship, we need to add the number of students who had a private scholarship (112) and the number of students who had both scholarships (17). This gives us a total of 129 students with a private scholarship. The rest of the students, who had either a government scholarship (80) or no scholarship (651), do not have a private scholarship.

209 students had only one of the two scholarships, so 209 - 129 = 80 students had a government scholarship.

So in total, 112 + 80 = 192 students had either a private or a government scholarship.

Therefore, 843 - 192 = 651 students did not have either a private or a government scholarship.

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The number of seeds that Frank will plant, expressed in algebraic form, is equal to 6b + 10.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are Given that, b and (5b + 10) are the seeds to be planted by Frank in different gardens, the number of seeds Frank is going to plant can be expressed in algebraic form by adding both expressions together.

Since Like terms with the same variables are added together.

Thus:

b + 5b + 10

6b + 10

Therefore, the number of seeds that Frank will plant, expressed in algebraic form;

6b + 10.

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As per the borrowed amount, the value of IRR is 6.40%

The term IRR is the internal rate of return is a metric used in financial analysis to estimate the profitability of potential investments.

Here we have know that Maggie green just borrowed $5,000. she is planning to pay it back in 5 equal installments of $1,200.

Now, we have to calculate the value of IRR,

The general form of the IRR formula is written as,

=> NPV = [tex]\sum\limits^T_{t=1} {\frac{C_t}{(1+r)^t} }\ -C_0[/tex]

where r is the discount rate / interest rate and T is the number of cash flow periods with t denoting a specific period, C0 is the initial investment while Ct is the return during period t.

Here we apply the values on it, then we get,

=> [tex]NPV = \sum\limits^5_{t=1} {\frac{1200_t}{(1+r)^t} }\ -5000[/tex]

When we simplify this one then we get,

=> Internal Rate of Return = 6.402%

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R-squared is calculated as the square of the linear correlation coefficient (r). In this case, the linear correlation coefficient is 0.817, so the R-squared can be calculated as follows:

R-squared = r^2 = 0.817^2 = 0.67

R-squared measures the proportion of variation in the dependent variable that is explained by the independent variable in a regression analysis. A value of R-squared close to 1 indicates that a large proportion of the variation in the dependent variable is explained by the independent variable, while a value close to 0 indicates the opposite.

In this case, a value of 0.67 for R-squared indicates that 67% of the variation in the dependent variable is explained by the independent variable, while the remaining 33% is unexplained.

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The current month's finance charge on Jada's credit card is found as : 7.48.

The provided data:

Calculation for the finance charge:

Daily interest rate = APR / 100 / 365

Daily interest rate = 0.18 / 365 = 0.00049315.

Daily finance charge = Carried unpaid balance × Daily interest rate

                                  =  $506.13 x  0.00049315

                                  = 0.249

Finance charge = Daily finance charge × Number of Days in Billing Cycle

                           = 0.249 x 30

                          = 7.48

Thus, the current month's finance charge on Jada's credit card is found as : 7.48.

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"none of these" is the transformation rule applied to this figure that is option B.

A transformation in geometry is an operation that moves, flips, or modifies a shape (called the preimage) to generate a new shape (called the image). A translation is a sort of transformation in which every point in a figure moves the same distance in the same direction. a logic principle that establishes the circumstances under which one assertion can be derived or legitimately inferred from one or more other statements, particularly in a codified language. Transformations are classified into four types: translation, reflection, rotation, and dilation. A transformation equation is an equation that transforms from one equation to another and whose provided roots are inverse to the roots in the given equation.

Here,

The transformation rule applied to this figure is "none of these" that is option B.

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3.5 capfuls of vitamin is required for the 350 liter fish tank, to keep the fish healthy.

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

To keep the fish healthy, 2 drops of vitamin is required per 5 liter of water. Hence, for 350 liter:

5 liter = 2 drops

350 liter = 350 liter * 2 drops per 5 liter = 140 drops

40 drops = 1 capful

Hence:

140 drops = 140 drops * 1 capful per 40 drops = 3.5 capfuls

3.5 capful is required for the 350 liter

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The correlation of coefficient is -0.988 and it is in negative form.

A correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.

The correlation coefficient is a value between -1 and 1 that indicates the strength and direction of the relationship between the two variables. A positive correlation means that as x increases, y also increases.

A negative correlation means that as x increases, y decreases. And a correlation of zero means that there is no relationship between x and y.

Here by using the correlation coefficient as  −0.988.

Therefore the correlation coefficient is negative, implying that the relationship between heights of a high jump bar and number of people successfully completing each jump is negative.

Complete Question:

The table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify and interpret the correlation coefficient.

Height (ft), x                  Completions, y

4                                          27

4.2                                       22

4.4                                       18

4.5                                       16

4.6                                       11

4.7                                       8

​

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The critical values for a two-sample z-test with a level of significance of 0.10 are -1.28 and 1.28.

This test is used to compare the proportions of two groups (males and females) who answered "yes" to the question "do you enjoy shopping for clothing?" The null hypothesis is that the proportion of males who enjoy shopping for clothing is equal to the proportion of females who enjoy shopping for clothing. The alternative hypothesis is that they are not equal.

To find the critical values, we use a standard normal table and find the z-scores that correspond to a cumulative probability of 0.05 (0.10/2) in both tails of the distribution. These values are -1.28 and 1.28.

In other words, if the calculated z-statistic is less than -1.28 or greater than 1.28, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportions of males and females who enjoy shopping for clothing are not equal.

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Use the formula: time = distance / speed

time = 7 km / 21 km/h = 1/3 hours

To convert hours into minutes, you can multiply the number of hours by the conversion factor 60.

1/3 x 60 = 20

It takes Moses 20 minutes to ride 7 km on a segway scooter at a top speed of 21 km/h.

Answer:  

Letter D

Step-by-step explanation:

not always zero

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A rashguard costs $25 at full price, which is calculated as 3x - 15 = 60.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given Blue Tide Swim Shop is having its annual summer sale,

rashguards sell for $5 less than the full price,

let the actual price of rashguards be x

price to be payed = x - 5

Miguel purchases 3 rashguards,

at cost  = $60

cost of 3 rashguards is 3(x - 5) = 3x - 15

3x - 15 = $60

3x = 60 + 15

3x = 75

x = 75/3

x = 25

cost of rashguards is $25.

Hence the actual cost is $25, and the equation is 3x - 15 = 60.

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(a) the value of y-intercepts is 70 (b) In what year did people born that year have an average life expectancy of 75 years= 1990 (c) the average life expectancy =76.5 years.

The average life expectancy y of a person born x years after 1960 can be approximated by the linear equation y = 1/6 x + 70.

(a) What interpretation can be given to the y-intercept of the graph?

we know that the standard form of a straight line is = y=mx+c

where c is y-intercepts,

So, we have y=0.1666x+70

here the value of C=70

hence, it is y intercepts=70

b)

In what year did people born that year have an average life expectancy of 75 years,

we have y=75

x=30

So year = 1960+30=1990.

c)  What is the average life expectancy of people born in 1999?

1999-1960=39=x

y=76.5 year.

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When introducing a data visualization to your audience, it is important to explain the context and the purpose of the visualization.

This will help your audience understand the visualization and its implications better. Additionally, you should quickly describe each graph and define each parameter to make sure that your audience is familiar with the data they are seeing. Finally, you should give your audience a few moments to process the information before you move on. This will help ensure that they can fully understand and appreciate the visualization.

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Based on the definition of similar polygons, the values of x and y are:

x = 10.7

y = 120°.

Similar polygon is a term used in geometry to describe two polygon shapes that have the same shape but not necessarily the same size.

Two polygon are said to be similar if and only if:

Therefore:

x + 4 / 22 = 12/18

18(x + 4) = (22)(12)

18x + 72 = 264

18x = 264 - 72

18x = 192

18x/18 = 192/18

x = 10.7

y = 180 - 60

y = 120°

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Step-by-step explanation: A square root function has a range of y greater-than-or-equal-to 0.

For example, the function f(x) = √x has a domain of x greater-than-or-equal-to 0 and a range of y greater-than-or-equal-to 0. This is because the square root of a positive number is always positive, and the square root of 0 is equal to 0. So, for any value of x greater-than-or-equal-to 0, the corresponding value of y will always be greater-than-or-equal-to 0.

Other functions that have a range of y greater-than-or-equal-to 0 include:

the absolute value function: f(x) = |x|

exponential functions with positive bases: f(x) = e^x, f(x) = 2^x, etc.

any linear function with a positive slope: f(x) = mx + b, where m > 0.

These are just a few examples of functions that have a range of y greater-than-or-equal-to 0.

Answer: 0.3

Step-by-step explanation:

      To find the constant of proportionality, you divide the y-value by the x-value.

            [tex]\displaystyle \frac{y}{x} =\frac{1.5}{5}= \frac{6}{20} \;\;=0.3[/tex]

Kapitan Tiago borrowed 560,000 × 60 % = 336,000 from the bank.

To find the amount borrowed, we multiply the balance Kapitan Tiago paid in cash by the loan percentage he obtained. The loan percentage is expressed as a decimal, so we multiply 560,000 by 0.6 to get 336,000.

This means Kapitan Tiago borrowed 336,000 from the bank and paid

560,000 - 336,000 = 224,000     in cash.

The total amount he spent on the car is

336,000 + 224,000 = 560,000.

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Answer:

Yes it does!

Step-by-step explanation:

Given, the growth of the bamboo changes over time. Therefore, the growth is directly proportional as it grows more with increase in time.

John has 6 quarters, 12 nickels, and 6 dimes, for a total of 24 coins. This is because he has twice as many nickels as quarters (12 nickels, 6 quarters), and two more dimes than nickels (12 nickels, 6 dimes). With this combination, the total value of all the coins would be $3.50.

To calculate the number of coins John has, we can use the following steps:

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Emily ran 731.6/12.4 = 59 meters per minute.

Hailey's plane climbed 1004.7/59.1 = 17 feet every second.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

1a.

Emily ran 731.6 meters in 12.4 minutes.

She ran 731.6/12.4 = 59 meters per minute.

1b.

Hailey's plane climbed 1,004.7 feet in 59.1 seconds.

Her plane climbed 1004.7/59.1 = 17 feet every second.

Therefore, all the required values are given above.

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You were on the right track, I totally understand why you'd get stuck where you are currently in the process. To start with, you technically found the wrong ratio between the two triangles. Your ratio is just 2x, while it should be 2x/5.

To start, let's find the ratio between triangle FEG and ABC by dividing angle F by and A:

[tex]R=\frac{2x}{5}[/tex]

Now, multiply angle B by this ratio:

[tex](x+4)(\frac{2x}{5} )=\frac{2x^2}{5}+\frac{8x}{5}=\frac{2x^2+8x}{5}[/tex]

We can now set this expression equal to angle E, as we have multiplied by the common ratio:

[tex]\frac{2x^2+8x}{5} =18[/tex]

This looks rather daunting, but let's keep calm... you can do this!!

Start by subtracting 18 from both sides:

[tex]\frac{2x^2+8x}{5}-18=0[/tex]

Now, let's get the whole expression under the denominator 5:

[tex]\frac{2x^2+8x-90}{5}=0[/tex]

Notice that the denominator can now be removed:

[tex]2x^2+8x-90=0[/tex]

Now, factor the equation (you could also use the quadratic eq if you want)

[tex]2(x-5)(x+9)=0[/tex]

Notice that we have two potential values for x (5 and -9).

Think about this logically... If we use -9 and plug it in for x, we will end up with values of -5 degrees for an angle, which is impossible! Therefore 5 is the only valid answer!

I encourage you to also approach the problem from a different angle and use the common factor (5/2x) and multiply it by 18 :)

This dilemma arises because oscillation requires two degrees of freedom while a equation one-dimensional system can never have more than one. An example of a constrained system is a basic harmonic oscillator.

This paradox results from the fact that oscillation needs two degrees of freedom whereas a one-dimensional system only has one. Position is the only variable in a one-dimensional system, hence oscillation is not feasible. But one example of a restricted system, where a constraint provides an additional degree of freedom, is a straightforward harmonic oscillator. The constraint in this scenario is a spring's force, which acts as a restoring force whenever the system deviates from its equilibrium state. The system can oscillate and move back and forth along the x-axis thanks to this restoring force. Thus, although having only one degree of freedom, the basic harmonic oscillator is an example of a one-dimensional system that can oscillate.

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The unsigned base 9 equivalent of the unsigned decimal integer value is 2233322

Decimal is a base 10 number system that we use in our daily lives to represent numbers.

In this case, the decimal number 6239124 is being converted to an unsigned base 9 equivalent.

To do this, we first divide the decimal number by 9 to get the first digit of the base 9 equivalent.

In this case, 6239124 divided by 9 is 693234 with a remainder of 2. So, the first digit of the base 9 equivalent is 2.

Next, we take the result of the division

=> (693234) / 9 = 76803 with a remainder of 3.

So, the second digit of the base 9 equivalent is 3.

We repeat this process until the result of the division is 0.

The final result is the base 9 equivalent of the decimal number 6239124. In this case, the base 9 equivalent is 2233322.

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Answer: Nora spent 11 ours working.

Step-by-step explanation: 3 + 2 + 2 + 4 = 11

Answer:

7

Step-by-step explanation:

meetings don't count

The rectangular coordinates form of r = 12 sinθ is x² + y² - 12y = 0

Given r = 12 sinθ and we are asked to convert this equation into rectangular coordinates.

The relation between polar coordinates (r,θ) and rectangular coordinates (x, y) is given by

                          x = r cosθ and y = r sinθ

Also, r² = (x² + y²)

r = 12 sinθ

Multiplying r both sides

r x r = 12 sinθ x r

   r² = 12r sinθ

We know r sinθ = y and r² = (x² + y²)

So, x² + y² = 12y

x² + y² - 12y = 0

Hence, the rectangular coordinates form is x² + y² - 12y = 0

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Using the definition of big o notation, t(n) = 32 * 4^n is O(f(n)) = 5^n with c = 26 and n0 = 1.

The definition of Big O notation states that a function t(n) is said to be O(f(n)) if there exist positive constants c and n0 such that |t(n)| <= c * |f(n)| for all n >= n0. In other words, t(n) grows no faster than f(n) as n becomes large.

To find the constants c and n0 that show that t(n) = 32 * 4^n is O(f(n)) = 5^n, we need to find a value of c and an n0 such that:

|32 * 4^n| <= c * |5^n|

for all n >= n0.

Let's start by finding a value for c that works for n = 1. We have:

|32 * 4^1| = 128 <= c * |5^1| = 5c

So, c >= 128 / 5 = 25.6.

Now let's try c = 26. We have:

|32 * 4^n| <= 26 * |5^n|

for all n >= 1.

Since 26 * |5^n| is an increasing function as n increases, we can conclude that:

t(n) = 32 * 4^n is O(f(n)) = 5^n

with c = 26 and n0 = 1.

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