Cecilia simplified an expression. Her work is shown below.

(6 and one-half + 2 and three-fourths) minus 1.5 times (4.5 divided by 0.5)
Step 1 9 and one-fourth minus 1.5 times (4.5 divided by 0.5)
Step 2 7.75 times (4.5 divided by 0.5)
Step 3 7.75 times 9
Step 4 69.75

Where did Cecilia make her first mistake?
step 1
step 2
step 3
step 4

WIll mark brainliest !

Step-by-step explanation:

the answer is 9 i hope it helps

The value of the function when x = 2 is 9

Functions are used to represent equations and graphs

The function is given as:

f(x) = 2x^2  - 3x + 7

When x =2, we have:

f(2) = 2(2)^2  - 3(2) + 7

Evaluate the exponent

f(2) = 2(4)  - 3(2) + 7

Evaluate the product

f(2) = 8  - 6 + 7

Evaluate the expression

f(2) = 9

Hence, the value of the function when x = 2 is 9

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Answer: To determine how much money Amber had in her account at the end, we need to subtract the total amount she withdrew from her initial balance.

Amber withdrew $36 each month for 6 months, so the total amount she withdrew is:

Total withdrawal = $36/month * 6 months = $216

To calculate the remaining balance, we subtract the total withdrawal from her initial balance:

Remaining balance = Initial balance - Total withdrawal

= $350 - $216

= $134

Therefore, at the end, Amber had $134 remaining in her account.

Based on probability calculations, approximately 7% of the people in the large group should obtain counts in the range of 20 to 30 aces when rolling a die 150 times.

When rolling a fair six-sided die, the probability of getting an ace (a single dot) is 1/6. Therefore, the probability of not getting an ace in a single roll is 5/6. To calculate the probability of obtaining a specific number of aces in 150 rolls, we can use the binomial distribution. In this case, the number of trials is 150, and the probability of success (getting an ace) in each trial is 1/6.

Using statistical calculations, we can determine the probability of obtaining counts between 20 and 30 aces. This involves summing the probabilities of getting 20, 21, 22, ..., 30 aces individually. This range of counts corresponds to a relatively small portion of the entire distribution. By calculating these probabilities and summing them, we find that the percentage of people who should obtain counts in the range 20 to 30 is approximately 7% of the total group size.

It's important to note that these calculations assume a fair six-sided die and independent rolls. The actual outcomes may vary due to chance, but on average, about 7% of the individuals in the large group would be expected to have counts in the specified range.

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Answer:

25 chords

Step-by-step explanation:

First, set up the ratio 40:8.

Now, make a proportion.

\(\frac{40}{8}\)=\(\frac{x}{5}\)

This proportion will give you x=25, so your answer is 25.

Hope this helps! Have a great day! :)

Answer:

she will play 31 chords

Step-by-step explanation:

Answer:

87.5$ since 25% is 1/4 87.5 is 1/4

Step-by-step explanation:

Answer:

$16

Steps:

12C + 28 = 220

12C = 220 - 28

12C = 192

C = 192÷12

C = 16

Each painting class costs $16

The cost of each painting class is $16.

Here,

The cost of the course covers 12 painting classes and she also bought a beginner's painting kit for $28.

Carla total paid = $220

We have to find the cost of each painting class.

What is Mathematical system?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Now,

Let the cost of each painting class = $x

And, The cost of the course covers 12 painting classes.

She also bought a beginner's painting kit for $28 and paid $220 in all.

Hence, The equation is;

12x + 28 = 220

12x = 220 - 28

12x = 192

x = 192 ÷ 12

x = 16

Therefore, The cost of each painting class is $16.

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Answer: R= 30.1

Step-by-step explanation: 10r = 7*43/1

10r= 301/1

10r= 301

10/10

R= 30.1

Answer:

this could be wrong but another guy said one a website it was 2500 but i haven’t got my results back yet

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

The value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to  y = 2x - 5 is 6.

No matter how far we extend a parallel line, it will always remain straight. Take a look at the parallel lines in the following illustration. Lines "p" and "q" are parallel to each other as are lines "a" and "b."

We know that parallel lines have same slope, so the slope of y = 2x - 5 is 2 according the y intercept form, y = mx + b

Now using the point-slope form we will find the line parallel to Point B (6, 8)

y − y₁ = m(x − x₁)

Put m as 2, y₁ as 8 and x₁ as 6, and we wil get

y − 8 = 2(x −6)

y = 2x − 4 or

2 = (y + 4)/x           (slope)

We will us point-slope form for point A(n, 4) too

y − 4 = 2(x −n)

y = 2x − 2n + 8 or

2 = (y - 8 + 2n)/x

As slope 2 is same in both points it means their equations are same too

(y + 4)/x  =  (y - 8 + 2n)/x

Lest solve for n

(y + 4)/x  =  (y - 8 + 2n)/x

y + 4 =  y - 8 + 2n

4 = - 8 + 2n

4 + 8 = 2n

2n = 12

n = 12/2

n = 6

Thus, the value of n for a line that passes through point A(n, 4) and point B(6, 8) and is parallel to  y = 2x - 5 is 6.

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Answer:

Step-by-step explanation:

commission from sale of $32,000 = $32,000 x 4% = $1,280

Suppose sales would double, comission would be doubled too.

Assume sales be S and commission be C

C = S * 4% (they have a linear positive relation)

if S double to 2S, new commission = (2S)*4% = 2*(S*4%) = 2 (old commission)

To conduct the study on the curriculum change for 5th graders in math, the statistical test that should be used is the t-test.

This test is appropriate when there are two groups to compare. The null hypothesis of the t-test is that the means of the two groups are equal while the alternative hypothesis is that they are not equal. To conduct the t-test, the mean and standard deviation of each group will be calculated. The t-test compares the means of the two groups to determine whether the difference between them is statistically significant.

Reporting of the findings of the t-test will be done through the use of graphs and charts. The results will be presented in a clear and concise manner, highlighting the key findings and their implications for the curriculum change. Any potential ethical dilemmas should also be addressed in the report. These may include issues such as informed consent, confidentiality, and potential biases in the data. It is important to ensure that all ethical guidelines are followed throughout the study to ensure the validity and reliability of the findings.

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The partial derivative \(\(f_x(x, y)\)\) of the function \(\(f(x, y)\) is \(y \cdot F'(yx)\),\) and the partial derivative \(\(f_y(x, y)\) is \(x \cdot F'(yx)\),\) where \(\(F'(t)\)\) is the derivative of an antiderivative of \(\(\cos(1t^2 + 6t - 8)\).\)

To find the partial derivatives of the function \(\(f(x, y) = \int_{0}^{yx} \cos(1t^2 + 6t - 8) \, dt\),\) we need to differentiate with respect to each variable separately. The partial derivative \(\(f_x\)\) represents the rate of change of \(\(f\)\) with respect to \(\(x\), and \(f_y\)\) represents the rate of change of \(\(f\) with respect to \(y\).\)

To find \(\(f_x(x, y)\),\) we differentiate \(\(f\)\) with respect to \(\(x\)\) while treating \(\(y\)\) as a constant. Similarly, to find \(\(f_y(x, y)\),\) we differentiate \(\(f\)\) with respect to \(\(y\)\) while treating \(\(x\)\) as a constant.

Since the function \(\(f\)\) involves an integral, we will need to apply the Fundamental Theorem of Calculus to find its partial derivatives. According to the theorem, if \(\(F(t)\)\) is an antiderivative of \(\(\cos(1t^2 + 6t - 8)\),\) then

\(\[f(x, y) = \int_{0}^{yx} \cos(1t^2 + 6t - 8) \, dt = F(yx) - F(0).\]\)

Now, let's find the partial derivatives \(\(f_x(x, y)\) and \(f_y(x, y)\)\) using the Fundamental Theorem of Calculus. Taking the derivative of \(\(f\)\) with respect to \(\(x\)\) gives us:

\(\[f_x(x, y) = \frac{\partial}{\partial x} \left[F(yx) - F(0)\right].\]\)

By applying the chain rule, we have:

\(\[f_x(x, y) = y \cdot F'(yx).\]\)

Similarly, taking the derivative of \(\(f\) with respect to \(y\)\) gives us:

\(\[f_y(x, y) = \frac{\partial}{\partial y} \left[F(yx) - F(0)\right].\]\)

Again, using the chain rule, we have:

\(\[f_y(x, y) = x \cdot F'(yx).\]\)

So, the partial derivatives of \(\(f(x, y)\) are \(f_x(x, y) = y \cdot F'(yx)\)\) and \(\(f_y(x, y) = x \cdot F'(yx)\), where \(F'(t)\)\) is the derivative of an antiderivative of \(\(\cos(1t^2 + 6t - 8)\).\)

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well, Not from tips that'd be 100% - 9% = 91%, so 91% of $7000.

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{91\% of 7000}}{\left( \cfrac{91}{100} \right)7000}\implies \text{\LARGE 6370}\)

After 60 minutes  both buckets dump water at the same time again.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

Given:

One bucket dumps water every 12 minutes. , while the other bucket dumps water every 10 minutes.

So, to find the When will both buckets dump water at the same time again we have to find the LCM

10 = 1 × 2 × 5

12 = 1 × 2 × 2 × 3

LCM = 1 × 2 × 2 × 3 × 5 = 60

Hence, After 60 minutes both buckets dump water at the same time again.

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The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer:

14.81%

Step-by-step explanation:

A fair six-sided dice has a total of six sides meaning that there are 6 possible outcomes for each dice roll. If two of the faces on the dice are red, then the possibility of rolling a red on a single dice roll would be 2/6, while the probability of rolling anything else would be 4/6 because there are 4 other sides left. Now if we roll three seperate dice, in order to calculate the probability of getting only one red face we need to multiply the probability of getting a red face on the first dice by the probability of the other two dice getting anything else.

2/6 * 4/6 * 4/6 = 32/216 or 0.1481

We can multiply this decimal by 100 to get the percentage value...

0.1481 * 100 = 14.81%

It is 180 degrees- hope this helps!

Answer:

- 1/2

Step-by-step explanation:

In order to find a slope intercept we need to use,

Equation : y= mx + b to find the slope (m)

Based on the information we can infer that Sophie is a Savvy Shopper.

A "savvy shopper" is an informal term used to refer to a person who is an expert in finding and taking advantage of the best deals and promotions when shopping. Another outstanding characteristic of these people is that they plan their purchases in advance and take advantage of promotions and discounts.

According to the above, we can infer that if Sophie is a bargain shopper who collects coupons and plans her route to take advantage of sales. She is a savvy shopper.

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The null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

Null hypothesis is a statistical hypothesis that claims there is no significant difference between a specified population parameter and the observed sample statistics. While alternative hypothesis is a statistical hypothesis that suggests that there is a significant difference between a specified population parameter and the observed sample statistics.In the given scenario, the null hypothesis and the alternative hypothesis will be:

Null hypothesis (H0): At most 70% of people who eat fast food more than 2x a week are overweight. (This means less than 70% are overweight)Alternative hypothesis (Ha): More than 70% of people who eat fast food more than 2x a week are overweight.

:We can evaluate the null hypothesis by testing the probability of a sample occurring, assuming the null hypothesis is true. If the probability of a sample is very low, it implies that it is unlikely that the sample was obtained assuming that the null hypothesis was true, and we can reject the null hypothesis and accept the alternative hypothesis

.In conclusion, the null hypothesis is that at most 70% of people who eat fast food more than 2x a week are overweight, and the alternative hypothesis is that more than 70% of people who eat fast food more than 2x a week are overweight.

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Answer:

x is equal to 73 since they are vertical angles

Answer:

Balblair! op opopopopoop

Given a parabola written in the form

The vertex is (h, k), the focus is (h, k+p) and the directrix is y = k - p.

Our parabola equation is

Therefore, if we compare with the form presented, the vertex of this parabola is

The focus is

And the directrix is

The P-value for a left-tailed hypothesis test with a test statistic of z = -1.40 is approximately 0.0808. Since the P-value (0.0808) is greater than the level of significance (α = 0.10), we do not have enough evidence to reject the null hypothesis at the 0.10 significance level.

To find the P-value for a left-tailed hypothesis test, we need to calculate the probability of observing a test statistic as extreme as or more extreme than the given value of z = -1.40 under the null hypothesis.

Using a standard normal distribution table or a statistical software, we can find that the cumulative probability for z = -1.40 is approximately 0.0808.

Comparing the P-value (0.0808) to the level of significance (α = 0.10), we see that the P-value is greater than α. Therefore, we do not have enough evidence to reject the null hypothesis at the 0.10 significance level.

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Answer:

Present age = 13 years

Step-by-step explanation:

Let the present age be x years.

14 years after age = (x + 14) years

4 years ago age = (x - 4)

According to the given information:

14 years after age = 3 times 4 years ago age

x + 14 = 3(x - 4)

x + 14 = 3x - 12

14 + 12 = 3x - x

26 = 2x

x = 26/2

x = 13 years

Thus, the present age is 13 years

Answer:

Step-by-step explanation:

When the stick is placed along the diagonal  of the cuboid , shortest possible length will extend out above top of the crate .

Length of the diagonal

= \(\sqrt{36^2+36^2+60^2}\)

= 78.69 cm

the length of the stick that extends out of the crate

= 90 - 78.69

= 11.31 cm

If θ be the angle made by stick with the base

cosθ = hypotenuse of base / diagonal of cuboid

=\(\frac{\sqrt{2}\times36 }{78.69}\)

= \(\frac{50.90 }{78.69}\)

θ = 50°

Answer: This is the answer to B) 47.9 degrees

Step-by-step explanation:

Pythagoras: a^2+b^2=c^2

36²+36²=C²

√2592=C

C=50.9cm

Used Trigonometry: SOH CAH TOA

Tan=Opposite/Adjacent

Tan=60/50.9

The angle stick makes when it meets the base:

Tan^-1(60/50.9)

=49.7˚

Answer:

165cm

Step-by-step explanation:

The Pythagorean Theorem is a fundamental concept that relates to the sides of a right-angled triangle, and it can also be used to understand the relationship between the areas of the squares constructed on the sides of the triangle.

The area of a square is given by the formula A = s², where s is the length of one of its sides. Therefore, the areas of the three squares are:

Area of the square with side a = a²

Area of the square with side b = b²

Area of the square with side c = c²

Now, let's compare the areas of the squares. We can start by subtracting the area of the square with side a from the area of the square with side c:

c² - a²

Using the Pythagorean Theorem, we know that c² = a² + b². Substituting this into the above expression, we get:

c² - a² = (a² + b²) - a² = b²

This tells us that the difference between the area of the square with side c and the area of the square with side a is equal to the area of the square with side b. In other words:

c² - a² = b²

This is known as the Pythagorean identity. It states that in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. We can also rearrange this identity to obtain the following:

c² = a² + b²

This is the Pythagorean Theorem that we are familiar with. Therefore, we can conclude that the relationship between the areas of the squares constructed on the sides of a right-angled triangle is given by the Pythagorean identity: the difference between the area of the square on the hypotenuse and the area of the square on the shorter side is equal to the area of the square on the other shorter side.

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