Judy will use 2 1/2 cups of flour for each cake she bakes. Judy has 10 cups of flour. What is the maximum number of cakes Judy can bake?

The calculation of the trigonometry illustrates that:

sin 45° = 1/✓2

cos45/tan 45 =

cos 45 sin 45 = 1/2

Opposite = 1

Adjacent = 1

Hypothenuse = ✓2

Tan 45 = opposite/adjacent = 1

Sin 45 = opposite/hypothenuse = 1/✓2

Cos 45 = adjacent/hypothenuse = 1/✓2

cos45/tan 45 = (1/✓2) / 1 = 1/✓2

Cos 45 sin 45 = 1/✓2 × 1/✓2 = 1/2

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The expression [tex]\sqrt{\frac{5}{x-1} }[/tex] is equivalent to the given quotient.

Option A is correct.

When we divide one number by another, the result is a quotient. Although a quotient can be greater than the divisor, it will never be greater than the dividend.

In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.

After the division has been done, the quotient is obtained. This signifies that the quotient is the result of dividing a dividend by a divisor.

According to the question,

[tex]\sqrt{25(x-1)}[/tex] ÷ [tex]\sqrt{5(x-1)^{2} }[/tex] =  5[tex]\sqrt{x-1}[/tex] ÷ (x-1)[tex]\sqrt{5}[/tex]

                                     =  [tex]\sqrt{\frac{5}{x-1} }[/tex]

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Answer:

A) 6.0

Step-by-step explanation:

First, total amount of hours, since average is sum of the numbers by how many numbers there is.

Day 1=8x2 hr

Day 2=6x1 hr

Day 3=4x2 hr

which is, 16+6+8=30

then divide 30 by how many days there is, which is 5 days.

30/5=6

The center of the circle is (-5, 4)

The circle equation is given as:

(x + 5)^2 + (y - 4)^2 = 9

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Center = (a, b)

By comparing both equations, we have

(a, b) = (-5, 4)

Hence, the center of the circle is (-5, 4)

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Answer:

monopoly, order 1

Step-by-step explanation:

because the x has just power of one that is why is monopoly and in order 1

The common base that can be used to rewrite each side of the equation is 2.

The common base that can be used to rewrite each side of the equation is as follows:

2ˣ⁺³ - 3 = 5

add 3 to both sides

2ˣ⁺³ - 3 + 3 = 5 + 3

2ˣ⁺³ = 8

Hence,

2ˣ⁺³ = 2³

Therefore, the common base that can be used to rewrite each side of the equation is 2.

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The inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

The standard form of the equation of the parabola is defined by the following expression:

y - k = C · (x - h)²     (1)

Where:

Now we proceed to find the vertex constant: (h, k) = (- 2, 2) and (x, y) = (- 4, 14)

14 - 2 = C · [- 4 - (- 2)]²

12 = C · (-2)

C = - 6

The equation of the parabola in vertex form is

y - 2 = - 6 · (x + 2)²

y = - 6 · (x + 2)² + 2

Then, the inequalty that represents the statement must be y < - 6 · (x + 2)² + 2. (Right choice: None)

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Answer:

y < 3(x + 2)2 + 2

Step-by-step explanation:

just do it

The points that represent this data are shown in the image attached below.

A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided in table above, the points that represent this data are shown in the image attached below.

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Answer:

please look at the picture

the person with the debt ratio that is higher than 18% can be found by dividing the person's debt by their income .

the necessary information is not given so a general explanation will be given.

the debt ratio is found by the formula:
= monthly debt payment / monthly gross income

this figure allows creditors to see if a person can affort to incur more debt based on how much of their gross monthly income is being used to service debt.

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Answer:

Step-by-step explanation:

(0,2)

Answer:

Step-by-step explanation

So, the graph goes through the points, (-3,0) and (2,0). 3 points on the graph can be (-3,0), (2,0), and (4,3)

No hay ninguno de los nimbers que no pertenezca a la secuencia.

Sabemos que una secuencia tiene que ver con un arreglo de números en un orden definido. Todos los números en una secuencia deben tener la misma razón común o diferencia común.

Si miramos todos los números que están escritos en la secuencia, la diferencia común aquí es seis. Se sigue entonces que todos los números son parte de la sucesión y no hay ninguno de los números que no pertenezca a la sucesión.

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Answer:

12 years old

Step-by-step explanation:

Set up the following equation:

x + 2 = 2(x - 5) (distribute the 2)

x + 2 = 2x - 10 (subtract 2 from both sides)

x = 2x - 12 (subtract 2x from both sides)

-x = -12 (multiply both sides by negative 1)

x = 12

Brainliest, please :)

Answer: 12

Step-by-step explanation:

Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.

The phrase "in two years" means when his age is 2 more than his current age, or x + 2.

The phrase "same as" represents equality. The expressions on both sides have the same value.

The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).

Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:

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

[tex]x+2=2x-10[/tex] [Distributive Property]

[tex]x+2-2x-2=2x-10-2x-2[/tex] [Adding -2x-2 to both sides]

[tex]-x=-12[/tex] [Combining like terms and simplifying]

[tex]x=12[/tex] [Multiplying both sides by -1 to remove the negative]

Hence, Billy's age is 12.

Answer:

Rafael earns $375

Andrew earns $340

Step-by-step explanation:

Here, we will set up a system of equations where r represents Rafael and a represents andrew.

r = a + 35

r + a = 715

Next, we substitute a + 35 for r in the second equation.

(a + 35) + a = 715 (combine like terms)

2a + 35 = 715 (subtract 35 from both sides)

2a = 680 (divide both sides by 2)

a = 340

To solve for r, we can plug 340 for a into either equation.

r = (340) + 35

r = 375

We can double check by plugging both values into the other equation.

375 + 340 = 715 (yes, it works!)

Brainliest, please :)

Answer:

4/5

Step-by-step explanation:

SImply use slope formula. We see the graph has defined points at (5, 4), and (-5, -4).

m=(Y2-Y1)/(X2-X1)

(4-(-4))/(5-(-5))=8/10

Simplify 8/10

=4/5

Answer:

U-A empty

Step-by-step explanation:

all in a is in u in u is in a therfore empty is found on u but not in a

Answer: [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

Step-by-step explanation:

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to [tex]y=5x+2[/tex] and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

Opposite Reciprocal of 5: [tex]-\frac{1}{5}[/tex]

Now that we have the slope and the point, we can use the point-slope form to get the equation of the perpendicular.

Point-Slope Form: [tex]y-y_1=m(x-x_1)[/tex] (m is slope, [tex]x_1[/tex] and [tex]y_1[/tex] are the point's coordinates)

[tex]y-0=-\frac{1}{5}(x-0)\\y=-\frac{1}{5}x[/tex]

Since we need to find a point on the original line that's closest to the origin, we need to find the intersection of the line and its perpendicular. We can do this by setting both lines equal to each other and solving for x and y.

[tex]5x+2=-\frac{1}{5}x\\25x+10=-x\\26x=-10\\x=-\frac{10}{26}\\x=-\frac{5}{13}[/tex]

Substituting x in any of the equations will give us y. Here, I will put it in the equation [tex]y=-\frac{1}{5}x[/tex]

[tex]y=-\frac{1}{5}*-\frac{5}{13}\\y=\frac{5}{65}\\y=\frac{1}{13}[/tex]

The closest point to the origin on the line [tex]y=5x+2[/tex] is [tex]\left(-\frac{5}{13}, \frac{1}{13}\right)[/tex]

The point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The given equation of a line is y=5x+2 ------(I)

The shortest distance from a point to a line is the perpendicular distance. The origin is essentially a point with coordinates (0,0); hence, we have to find the equation of the line that's both perpendicular to y=5x+2 and crosses the origin.

We can do this by recognizing that slope of a perpendicular line is the opposite reciprocal of the slope of the original line.

So, slope of perpendicular line is -1/5

The equation of the point slope form is: (y - y1) = m(x - x1)

Now, substitute m=-1/5 and (x, y)=(0, 0), we get

y-0=-1/5 (x-0)

y=-1/5 x -----(II)

Equate equation (I) and (II), we get

5x+2=-1/5 x

⇒ -x=25x+10

⇒ -26x=10

⇒ x= -5/13

So, y=-1/5 x =1/13

Therefore, the point on the line y = 5x + 2 that is closest to the origin is (-5/13, 1/13).

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Answer:

[tex]x^2 + 10x + 25[/tex]

Step-by-step explanation:

Hello!

Formula: [tex](a +b)^2 = a^2 + 2ab + b^2[/tex]

Plug it into the formula and simplify.

The answer is the first option: [tex]x^2 + 10x + 25[/tex].

Answer:

x^2-10x+25

Step-by-step explanation:

This is the correct answer

The measure of angle C (m ∠C) is 40°

From the question, we are to determine the measure of angle C (m ∠C)

In any given triangle, the sum of all the angles is 180°

Thus,

In ΔABC, the angles sum up to 180°

That is,

∠A + ∠B + ∠C = 180°

From the given information,

m ∠A = 80°, m ∠B = 60°

Thus,

80° + 60° + m ∠C = 180°

140° + m ∠C = 180°

m ∠C = 180° - 140°

m ∠C = 40°

Hence, the measure of angle C (m ∠C) is 40°

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The radius of the given cylinder with a volume of 200 mm³ and a height of 17mm is: 1.93 mm.

The formula for finding the volume of any cylinder is given as: πr²h, where r is the radius and h is the height of the cylinder.

Given the following:

Volume = 200 mm³

Height (h) = 17 mm

Radius (r) = ?

Plug the values into the formula for volume

πr²(17) = 200

r² = 200/17π

r² = 3.74

r = 1.93 mm

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Answer:

31 units

Step-by-step explanation:

If a quadrilateral has a pair of sides that is both parallel and congruent, then the quadrilateral is a parallelogram.

Sides AD and BC are given as parallel.

If they are also congruent, then quadrilateral ABCD is a parallelogram.

3x + 7 = 5x - 9

-2x = -16

x = 8

AD = 3x + 7

AD = 3(8) + 7

AD = 31

Answer: 31 units

Using conditional probability, it is found that:

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

For this problem, we are given that:

Then:

[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]

[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

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The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)

Herein we have a description of an irregular quadrilateral, whose area must be determined by adding the areas of minor quadrilaterals and triangles that are part of it. The area is now determined:

A = 0.5 · (24 cm) · (7 cm) + 0.5 · (15 cm) · (20 cm)

A = 234 cm²

The area of the irregular quadrilateral ABCD is equal to 234 square centimeters. (Correct choice: C)

The picture with the quadrilateral is missing and is included as attachment.

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Answer:

15m

Step-by-step explanation:

Let w be the width, l the length and p the perimeter.

We know, by definition, that p = 2w + 2l. We also know that p = 80m and l = 25m.

So we can re-write the perimeter formula as:

80 = 2w + 50

2w = 30

w = 15m

So we now know that the width is 15m.

The sweatshirt size which the vendor should bring more of by virtue of that which is most likely to be sold is; Choice A; Extra-large.

If follows from the task content that the

ratio of extralarge shirts sold relative to the quantity he had to sell is

= 99/108

= 11/12,

This is a ratio which is larger than any other shirt.

Consequently, the vendor must bring more of the X-large shirts to avoid running out of them.

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The equation of the line is y = -3/2x + 10

The given parameters are:

Slope, m = -3/2

Point, (x, y) = (10, -5)

The line equation is represented as

y = mx + b

Substitute the given parameters in the equation

-5 = -3/2 * 10 + b

This gives

-5 = -15 + b

Add 15 to both sides

b = 10

So, we have:

y = -3/2x + 10

Hence, the equation of the line is y = -3/2x + 10

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Using the z-distribution, the test statistic is:

c) -2.63.

At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, we test if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

For the distribution of differences, it is given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

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Answer:

t=150

Step-by-step explanation:

50+100=150

50×12=600

Answer:

25/36, or .694444

Step-by-step explanation:

First, let's convert 6" to inches.

That gives us 72. After we convert 4'2" into inches, we get 50.

This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:

50/72 = 25/36 = .6944444

By applying trigonometric expression and direct comparison, we conclude that a = 2 such cos 255° - cos 195° = √a / 2

In this question we need to simplify a trigonometric expression in order to find the value of a. In this case, we need to use the following formula:

[tex]\cos \theta - \cos \xi = - 2\cdot \sin \left(\frac{\theta + \xi}{2} \right)\cdot \sin \left(\frac{\theta - \xi}{2} \right)[/tex]

Then,

cos 255° - cos 195° = - 2 · sin 225° · sin 30°

cos 255° - cos 195° = - 2 · sin (- 135°) · sin 30°

cos 255° - cos 195° = 2 · sin 135° · sin 30°

cos 255° - cos 195° = 2 · (√2 / 2) · (1/2)

cos 255° - cos 195° = √2 / 2

Then, by direct comparison we find that a = 2.

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