Drag each equation to show if it could be a correct first step to solving the
equation
3(x+8)= 42.


Put in Yes, No, or Not Enough Information category.

Answer:

Step-by-step explanation:

\(y^2-10y+30=\\y^2-2(y)(5)+5^2-5^2+30=\\(y-5)^2-25+30=\\(y-5)^2+5\)

\((y-5)^2\geq 0\\\Rightarrow\ (y-5)^2+5 > 0\\Thus,\ y^2-10y+30 > 0\)

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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Answer:

161.5 miles

Step-by-step explanation:

Given

\(Trip = 533\ miles\)

\(Gas = 105\ miles\)

Required

Determine the distance left until you stop to eat

From the question, we understand that you plan to eat at half the trip.

This is calculated as thus;

\(Eat = \frac{1}{2} * Trip\)

\(Eat = \frac{1}{2} * 533\)

\(Eat = 266.5\)

Next:

Subtract the distance you got gas from the distance to eat.

\(Distance = 266.5 - 105\)

\(Distance = 161.5\ miles\)

Answer:

C

Step-by-step explanation:

The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted to mathematical equation

The left over is calculated is 3/8

therefore 5/8 of the pizza is left for Saturday

On Saturday she ate 1/4 of the pizza

= 1/4 × 3/8

= 3/32

therefore Miah ate 3/32 of the whole pizza on Saturday.

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Answer: The last option.

Step-by-step explanation:

         The statement that can be used to prove that vertical angles ∠1 and ∠3 are congruent is;

             m∠1 + m∠2 = m∠2 + m∠3

       This is because we know that m∠1 + m∠2 is a straight line and that m∠2 + m∠3 is a straight line. Straight lines are equal to 180 degrees, so the vertical angles must be congruent.

Answer:

(-5,-8.5)

Step-by-step explanation:

-3-7=-10

-9-8=-17

-10/2=-5

-17/2=8.5

I'm NGL dawg, your comments don't make sense but that's the mid point for (-3,-9) (-7,-8).

Answer:

-13

Step-by-step explanation:

f(-2) = 3(-2) - 7

f(-2) = -6 - 7

f(-2) = -13

f(-2) means to replace x with -2 in the equation and solve:

3(-2) - 7 = -6 - 7 = -13

The answer is -13

The weight of the bag =

Weight of 2 pairs of shoes  + weight of 10 items of regular clothes + weight of 2 coats.

A weight characteristic is a mathematical tool used when appearing a sum, critical, or average to provide some factors extra "weight" or impact on the result than different factors within the equal set.

Weight Value is the basis of the overall progress calculation processes used to determine the weight of each phase in the project. It is measured based on the distribution of weight values and obtained by multiplying the weight value of each task in the project.

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Answer:

not meeee

Step-by-step explanation:

giv brainliest pls

Answer:

yeah

Step-by-step explanation:

i am

The ogive is a line graph that plots the cumulative relative frequency distribution.

An ogive, also known as a cumulative frequency polygon, is a line graph that shows the cumulative frequency distribution of a data set. The cumulative frequency is calculated by adding up the frequencies of each value up to a certain point in the data set.

The cumulative relative frequency is calculated by dividing the cumulative frequency by the total number of observations in the data set. The ogive plots these cumulative relative frequencies against the corresponding values in the data set, usually on the x-axis.

By plotting the cumulative relative frequencies, the ogive shows how the data is distributed over the entire range of values. It can be used to identify patterns in the data, such as whether it is skewed or symmetrical. It is also useful for determining percentiles, as the percentile for a given value can be read directly from the ogive.

Overall, the ogive is a helpful tool for summarizing and visualizing the distribution of a data set, particularly when dealing with large data sets or complex distributions.

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Based on the information given, it can be noted that the average balance for the period given will be $5712.04.

The average balance will be:

= 30(5712.04) / 30.

= $5712.04

The finance charge will be;

= 14% × $5712.04

= 0.14 × $5712.04

= $79.97.

The average daily balance will be;

= [(29 × 712.04) + 5712.04] / 30

= (20649.16 + 5712.04) / 30

= 878.71

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A. The average daily balance for the 30-day period if the down payment is made on the last day is $1,064.55.

B. The finance charge on the average daily balance is $16.34.

C. Irina cannot save any finance charges by making the down payment on the last day; instead, she would pay an additional $3.33 compared to making it on the first day.

Let us consider two scenarios:

Scenario 1: Irina's daily balance for the first 29 days of the billing cycle is $712.04, and on the 30th day, it increases to $5,712.04.

Scenario 2: Irina's daily balance remains at $712.04 for all 30 days of the billing cycle.

Let's calculate the average daily balance and the finance charge for each scenario:

A. Average Daily Balance:

Scenario 1:

(29 × 712.04 + 5712.04) / 30 = $1,064.55 (rounded to the nearest cent)

Scenario 2:

30 × 712.04 / 30 = $712.04

B. Finance Charge:

To calculate the finance charge, we need to multiply the average daily balance by the APR (annual percentage rate) and divide it by the number of days in a year (365).

Finance charge for Scenario 1:

($1,064.55 × 0.168) / 365 × 30 = $16.34 (rounded to the nearest cent)

Finance charge for Scenario 2:

($712.04 × 0.168) / 365 × 30 = $13.01 (rounded to the nearest cent)

C. Savings in Finance Charges:

The savings in finance charges if Irina makes the down payment on the last day, as compared to making it on the first day, can be calculated by subtracting the finance charge of Scenario 1 from Scenario 2.

Savings in finance charges:

$13.01 - $16.34 = -$3.33 (rounded to the nearest cent)

Since the result is negative, it means that Irina would pay $3.33 more in finance charges if she makes the down payment on the last day compared to making it on the first day.

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We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

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The arc in the circle is given as follows:

Minor arc Arc KLA.

An arc can be classified as either a minor arc or a major arc, depending on it's angle measures, as follows:

The arc for this problem is given as follows:

KLA.

The arc measure is less than half the circumference, that is, less than 180º, hence the arc is classified as a minor arc.

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Answer:

v= 37.8 miles/ 2.7 hours = 14 miles/hrs

Please check my other articles in my site, just copy and paste this word to google search engine: learningandassignments diy4pro.

Hope it helps you.

Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

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\( \boxed{ \red{ \mathfrak{Perimeter \: of \: semi - circle =\pi r + 2r }}}\)

\( \pink \longmapsto \purple { \mathfrak { Perimeter= \frac{22}{7}\times11 +22 }}\)

\( \pink \longmapsto \purple { \mathfrak { Perimeter= \frac{242}{7}+22 }}\)

\( \pink \longmapsto \purple { \mathfrak { Perimeter= \frac{396}{7}}}\)

\( \pink \longmapsto \purple { \mathfrak { Perimeter= 56.5 \: cm}}\)

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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\( \large \bf \implies{32 {m}^{15} {n}^{10} }\)

\(\bf \longrightarrow{(2m^{3}n^{2})^{5} } \\ \\ \bf \longrightarrow {2}^{5} \times ( {m}^{3})^{5} \times ( {n}^{2})^{5} \\ \\ \bf \longrightarrow32( {m}^{3})^{5}( {n}^{2})^{5} \\ \\ \bf \longrightarrow32 {m}^{15} {n}^{10} \)

Note : We have used the two exponent rules:

\((1) \: \: \large \bf \boxed{ \bf \green{(ab)^{n} = {a}^{n} \times {b}^{n} }}\)

\((2) \: \: \large \bf \boxed{ \bf \green{(a^{n})^{m} = {a}^{nm} }}\)

Answer:

idk

Step-by-step explanation:

ask oggle

Answer:

Odd

Step-by-step explanation:

The answer to the equation is 1,859, making the answer odd.

Answer:

\(y = 46x + 0\)

Step-by-step explanation:

The equation of a line follows the following format

\(y = mx + c\)

Note m= the gradient of the line or the slope of the line. To find the gradient it is

\(m = \frac{rise}{run} \)

On this graph the

\(rise \: = 460 \: \\ and \\ run = 10 \\ \\ m = \frac{460}{10} \\ m = 46\)

After finding the gradient we can now find the equation of the line. We can use any point on the line in order to do this, in that case lets use the point (10, 460)

\(y = 460 \: \: \: \: \: \: x = 10 \: \: \: \: \: m = 46\\ y = mx + c \\ 460 = (46)(10) + c \\ 460 = 460 + c \\ 460 - 460 = c \\ 0 = c\)

\(y = 46x + 0\)

The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

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Answer: Yes.

Step-by-step explanation: 20% of 100 would translate into .2 out of 1

Answer:

Yes, coz 20%=20/100

Ans solving 2/100 will give you 0.2

So ya, that's right!

Answer:

A prime number has exactly two factors, 1 and itself. For example, 13 is a prime number because the only factors of 13 are 1 and 13

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The data analyst should use a bar chart for the visualization that makes it easy to show which of the top ten most populous cities in North Carolina have a population below 250,000 people.

A bar chart is a graph that represents categorical data with rectangular bars.

The height or length of the bars is proportional to the values they represent.

The bars can be plotted either horizontally or vertically based on the data being presented.

They are frequently used to compare values across different categories by plotting the categories along the horizontal axis and the values along the vertical axis.

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The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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current flowing through the light bulb is 2.2 Amperes

Step by step explanation:

Step 1:

Given the voltage = 60 Volts and power = 174 Watts.

Find the current using the formula , P = V . l

=> l = P/V=60/174= 0.3448275862

A basis for the subspace is {1, \(x^2\)}, and the dimension of the subspace is 2.

a. To find a basis for the subspace {a(1 + x) + b(x + x^2) : a, b ∈ R} of P2, we need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set a = 1 and b = 0, we get the polynomial 1 + x, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1 + x, x + x^2}, and the dimension of the subspace is 2.

b. To find a basis for the subspace {(a + b(x + x^2)) : a, b ∈ R} of P2, we again need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set b = 0, we get the polynomial a, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x + x^2}, and the dimension of the subspace is 2.

c. To find a basis for the subspace {p(x) : p(1) = 0}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(1) = 0 must have a factor of (x - 1). Therefore, we can write any polynomial in the subspace as p(x) = (x - 1)q(x), where q(x) is a polynomial of degree 1 or 0.

If we set q(x) = 1, we get the polynomial x - 1, which is in the subspace. If we set q(x) = 0, we get the zero polynomial, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {x - 1}, and the dimension of the subspace is 1.

d. To find a basis for the subspace {p(x) : p(x) = p(-x)}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(x) = p(-x) must be an even function. Therefore, we can write any polynomial in the subspace as p(x) = a + bx^2, where a and b are constants.

If we set a = 1 and b = 0, we get the polynomial 1, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x^2}, and the dimension of the subspace is 2.

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