Ashley decorates cakes and uses red icing to write a message on the cakes. she uses 10 1/2 ounces of red icing to write a message on 3 1/2 cakes . Based on this rate how many ounces of red icing are needed to write a message on one cake ?

The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.

Let's say there are "m" appetizer options and "n" vegetable options on the menu.

Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:

m x n ways

So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.

Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.

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Using division operation, if Amanda and her two friends split the total cost of renting a truck equally, Amanda will pay $47.50.

The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.

The division operation involves the dividend (the total cost) divided by the divisor (3 friends), which results in a quotient.

Fixed cost for renting a truck = $120

The variable cost per mile = $0.50

The total miles Amanda and her two friends drove = 45 miles

The variable cost for 45 miles = $22.50 ($0.50 x 45)

The total costs = Fixed + Variable Costs

= $142.50

Cost paid by Amanda = $47.50 ($142.50/3)

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The fixed cost for renting a truck is $120 with a variable cost per mile of $0.50.

When the input of the function is -3, the output of the function is -4

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

The graph

On the graph, we have the following reading at x = -3

(x, y) = (-3, -4)

This means that when x = -3, the value of y is -3

So, the conclusion is that

An input of -3, gives an output of the function is -4

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If the similar sides and angles of two triangles are proportionate, then the triangles are similar.

We must assess if two triangles have the same shape but perhaps different sizes in order to determine their similarity. The triangles are similar if their corresponding sides are proportionate. The triangles are not comparable if they are not proportionate. We only need to determine whether two triangles' respective sides are proportionate if we are given two triangles and are aware that their corresponding angles are congruent.

In conclusion, in order to establish whether two triangles are comparable, we must look at both the proportionality of the respective sides and the congruency of the corresponding angles. The triangles are similar if both requirements are satisfied, and we can create a similarity assertion by using the matching triangle vertices.

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Answer:

150

Step-by-step explanation:

5/6= ?/180

We can use cross-products to solve.

5 * 180 = 6 * ?

Divide each side by 6.

5 * 180/6 = ?

5 * 30 = ?

150

The missing number is 150.

Answer:

150/180

Step-by-step explanation:

Solution by Cross Multiplication;

The equation:

[tex]\frac{5}{6} = \frac{x}{180}[/tex]

The cross-product is:  

5(180)  =  6(x)

Solving for x:

x = [tex]\frac{5(180)}{6} \\[/tex]

x = 150

The number 402 would be represented as 4|02.A stem-and-leaf plot is a graphical representation of a data set that is used to show its distribution.

The number 402 would be represented as 4|02. A stem-and-leaf plot is a way of organizing data into numerical order. It separates the numbers into two parts, the stem, which is the first digit or digits, and the leaf, which is the last digit or digits. The stem is listed on the left side and the leaf is listed on the right side. In this case, the stem would be 4 and the leaf would be 02, so the number 402 would be represented as 4|02.

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Answer:4l02

Step-by-step explanation: mark me brainiest ;]

The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,

We need to find ∠ 1

Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,

Therefore,

3x-10 = 2x+5

x = 15

Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,

Therefore,

∠ 1 = 2(15)+5

∠ 1 = 35°

Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

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The figure was not given so the figure is attached.

The depth d of the crater is 714 m. The solution has been obtained by using trigonometry.

What is trigonometry?

The area of mathematics known as trigonometry is concerned with the study of the sides, angles, and connections of the right-angle triangle.

We are given a figure which shows that the sun's rays are falling at an angle of 55° and the base is given as 500 m.

Using trigonometry,

We know that tan theta = opposite side/ adjacent side

So,

⇒tan θ = d/500

Here, θ = 55°

So,

⇒tan 55° = d/500

⇒x = 500 tan 55°

⇒x = 500 * 1.428148

⇒x ≈ 714.074

⇒x ≈ 714 m

Hence, the depth d of the crater is 714 m.

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The graph of the function is horizontal when the value of the Porsche stays even.

Staying even means that the value of the car does not change, hence it is constant.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (3 {m}^{5} )(4m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (3 \times 4)(m {}^{5} \times m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{(5 + 9)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{14} [/tex]

So, The correct choice is B.) 12 m¹⁴

Answer:

15

Step-by-step explanation:

The value of the lettered sides of the triangle are n=4, m=3

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry

From the Triangles, <BAC = <DBC                         given

⇒ΔBAD ≅ ΔDBC       (SAS)

/BA/ =/BD/ = 3 units

Also, /BC/ = /AD/ = 4 units

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The vertical difference in height between

i. A and B = 1.55

ii. B and C = 1.27

iii. A and C. = 2.82

the angle of elevation from A to C

The vertical difference in height is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The directions describes a right angle triangle o

A and B

sin 15 = vertical difference / 6

vertical difference = 6 sin 15

vertical difference = 1.55

B and C

sin 25 = vertical difference / 3

vertical difference = 3 sin 25

vertical difference = 1.27

A and C

A to B + B to C

= 1.55 + 1.27

= 2.82

angle of elevation from A to C

sin x = 2.82 / 5

x = arc sin (2.82/5)

x = 34.33 degrees

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The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)

In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.

The formula for NORM.INV function is:

= NORM.INV(1-A, mu, sigma)

where:

A is the right-tail probability (or area)

mu is the mean of the distribution

sigma is the standard deviation

The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.

Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.

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Answer:

I believe Edgar payed $84 for the tickets.

Step-by-step explanation:

12(4)=48

6(6)=36

48+36=84

Answer: 44, -14, 4

Step-by-step explanation:

plug the f(x) into the x and solve itself.

(5)^2 + 3(5) + 4 = 44

(-3)^2 + 3(-3) + 4 = -14

(0)^2 + 3(0) + 4 = 4

Answer:

The height of the kite above the ground is; approximately 50.69 feet.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

The height of his hands above the ground, h is given by 3 feet

Angle of elevation of the string (above the horizontal), θ = 32°

Length of the string, l is given as 90 feet

The height of the kite above the ground is given by trigonometric ratios as ;

Sin∅ =h /90

Sin 32°= h/90

0.52 =h /90 (Sin32°= 0.52)

so h= 47.69 feet

Then height from ground is (H) = 3 +47.69  

H = 50.69 feet

The height of the kite above the ground ,  ≈ 50.69 feet

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Step-by-step explanation:

The number of choices for all the possible passwords are 43,056,000

Given, we have to make a password which includes 4 characters and 4 even digits. And none of the characters or digits can be used more than once. So, For the first character we have 26 choices as we can use any character from the alphabet. For the 2nd character we get 25 choices as we cant choose the first character already twice. Similarly, for 3rd character we get 24 choices and for 4th character we get 23 choices.

Now for the digits, we can only use even digits 0,2,4,6,8 with no repetition allowed. Therefore, for first digit we can choose any digit so we get 5 choices. For the 2nd digit we get 4 choices. For the 3rd digit we get 3 choices. For the 4th digit we get 2 choices.

Noe, to find all the possible combinations , we just need to multiply all the choices :

⇒ 26 x 25 x 24 x 23 x 5 x 4 x 3 x 2

⇒ 43,056,000

Therefore, the total number of all the possible combination of passwords according to the given condition is 43,056,000.

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In the given case the set of 56 students who returned surveys is an example of a sample

A sample would be the 56 students who responded to the surveys. A sample is a portion of the population that is chosen for a study in research. American college students would be the population in this scenario. The 56 students who returned the surveys were chosen at random for the sample by the researcher.

The researcher is attempting to guarantee that the sample is representative of the greater population of American college students by utilising a random selection process. The researcher discovered that these students spend an average of 4.1 hours per week working on course material outside of class based on the data collected from the sample. This is an example of a descriptive statistic that provides a summary of the information gleaned from the sample.

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The exponential function for the  population is X = 203.[tex]e^{0.0107.t}[/tex]

The formula for an exponential function is f (x) = ax, where x is a variable and a is a constant that serves as the function's base and must be greater than 0.

Let be supposed that population can be modelled by means of the following exponential function:

X = A.[tex]e^{Bt}[/tex]

Where:

t - Time, measured in years. Where t = 0 for 1970.

A - Initial population, in millions inhabitants.

B - Exponential rate constant, in years.

X - Population, in millions inhabitants.

Each constant is found hereafter:

X = A.[tex]e^{Bt}[/tex]

203 = A.[tex]e^{B*0}[/tex]

203 = A[tex]e^{0}[/tex]

A= 203

X = A.[tex]e^{Bt}[/tex]

X = 203[tex]e^{B.10}[/tex]

226 = 203[tex]e^{B.10}[/tex]

B = 1/10(ln(226/203))

B = 0.0107

The exponential function for the  population is:

X = 203.[tex]e^{0.0107.t}[/tex]

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The values of the means for the two types of glasses suggest about the shape of glasses used is 22ml on average.

When it comes to pouring drinks, bartenders are expected to pour a specific amount of liquid into each glass. However, there may be some variation in the amount poured depending on the shape of the glass. In this scenario, we have data on the actual amount poured by bartenders into a short, wide glass when asked to pour 44.3 ml. We will use this data to calculate the mean and standard deviation and interpret their values.

The mean is the average amount poured into the short, wide glass. To find the mean, we add up all the amounts poured and divide by the number of samples. Using the data provided, we get a mean of 57.889 ml, rounded to three decimal places.

However, the mean doesn't tell us the whole story. We also need to consider the standard deviation, which tells us how much the amounts poured vary from the mean.

To calculate the standard deviation, we first need to find the variance. We calculate this by subtracting the mean from each amount poured, squaring the differences, adding them up, and dividing by the number of samples minus one. Using the data provided, we get a variance of 479.716 ml², rounded to three decimal places.

To get the standard deviation, we take the square root of the variance. Using the data provided, we get a standard deviation of 21.904 ml, rounded to three decimal places.

Interpreting the values of the mean and standard deviation, we can say that a typical amount poured into a short, wide glass is 57.889 ml, while a typical deviation from the mean amount poured is 21.904 ml. This means that the amounts poured vary by about 22 ml on average, which could be due to differences in pouring technique or the shape of the glass.

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In the illustration given above, the length and the diameter of the shaft would be = 21.8 in and 7/8 in respectively.

The total length of the shaft can be calculated through the addition of the various given lengths along the shaft such as follows:

= 5⅛ + 5 + 7⅝ + 4 1/16

First convert all the mixed fraction into single fraction;

= 41/8 + 5/1 + 61/8 + 65/16

= 82+80+122+65/16

= 349/16

= 21.8 in.

The diameter of the shaft can be calculated as follows;

= 7¼ - (3 3/16 + 3 3/16 )

First convert all the mixed fraction into single fraction;

= 29/4 - (51/16 + 51/16)

= 29/4 - 102/16

= 116-102/16

= 14/16

= 7/8 in.

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Answer:

24 edges, on the 10 faced prism

Answer:

Helena can paint approximately 32 of these cylinders complete

Step-by-step explanation:

The surface area of a cylinder can be found using the formula:

Surface Area = 2πr(r + h), where r is the radius and h is the height (or length) of the cylinder.

For a cylinder with a radius of 5 cm and a length of 3 cm, the surface area is:

Surface Area = 2π x 5 x (5 + 3) = 2π x 5 x 8 = 80π cm²

So, the surface area of one cylinder is 80π cm². To find the number of cylinders that Helena can paint, we can divide her total paint coverage by the surface area of one cylinder:

2500 cm² ÷ 80π cm² = 31.83 (approximately 32 cylinders).

So, Helena can paint approximately 32 of these cylinders completel

Answer:

Step-by-step explanation:

Bottom right is the correct graph.  Plot the line y ≤ 3x-4 and shade the area below the solid line.  Next plot y < -2x +3 and shade the area below the dashed line.  Where the 2 shaded areas intersect is the solution.  Bottom right graph show this.

Answer:

  ±1.007%

Step-by-step explanation:

You want the relative error in the computed value of 1/P -1/Q when P=1.80 and Q=2.91.

Each of P and Q is specified to the hundredths place, so the errors in each of P and Q will be half of a hundredth, or 0.005. The maximum value of P or Q will be 0.005 more than the given value, and the minimum will be 0.005 less.

The maximum and minimum of the computation will be had when P and Q are at their opposite extremes: one is a maximum when the other is a minimum.

Max difference = 1/1.795 -1/2.915 ≈ 0.21404

Min difference = 1/1.805 -1/2.905 ≈ 0.20978

The relative error in the computed value can be found a couple of ways. One is to compare the maximum and minimum computed values with the nominal computed value.

Here, we choose to compare half the difference in the computed values to the average of the computed values. That way, we can describe the error as symmetrical about that average;

  ((0.21404 -0.20978)/2) / ((0.21404 +0.20978)/2) = relative error

  = (0.21404 -0.20978) / (0.21404 +0.20978) ≈ 0.01007

The relative error is about ±1.007%.

__

Additional comment

Another way to compute the error is by looking at the derivatives. The relative error found that way is ...

  RE = -∆P(Q/P(Q -P)) +∆Q(P/Q(Q -P))

where ∆P and ∆Q are ±0.005.

The maximum relative error found this way is about ±1.00686% compared to the ±1.00685% computed above.

If you compare the possible error to the nominal value, it is not symmetrical: -1.00532% to 1.00841%.

Looking at the above expression for RE, you see that the multiplier of the relative error in P is Q/(Q-P), while the multiplier of the relative error in Q is P/(Q-P). That is, errors in P have a much larger effect than errors in Q.