a recipe for cookies says 2/3 of a cup of sugar will be enough to feed 3/4 of my class. how much sugar will i need to make enough cookies to feed my whole class?

The measure of angle Z is 34°, side length of YZ is 34.1, and the side length of XZ is 41.1. The correct option is the third option ∠Z = 34°, YZ = 34.1, XZ = 41.1

From the question, we are to determine the angles measures of and the side measures of the given triangle XYZ

From the given information,

∠Y = 90°

XY = 23

∠X = 56°

First, we will determine the measure of angle Z

m ∠X + m ∠Y + m ∠Z = 180° (Sum of angles in triangle)

56° + 90° + m ∠Z = 180°

m ∠Z = 180° - 56° - 90°

m ∠Z = 34°

Now, since the measure of one of the angles is 90°, ΔXYZ is a right triangle.

Thus,

From SOH CAH TOA, we can write that

tan X = |YZ| / |XY|

∴ tan 56° = |YZ| / 23

|YZ| = 23 × tan 56°

|YZ| = 34.0989

|YZ| ≈ 34.1

Also,

cos X = |XY| / |XZ|

cos 56° = 23 / |XZ|

|XZ| = 23 ÷ cos 56°

|XZ| = 41.1307

|XZ| ≈ 41.1

Hence, ∠Z = 34°, |YZ| = 34.1, and |XZ| = 41.1

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Answer:

The prices of apples this week is $1.40.

Step-by-step explanation:

First, convert the 20% into 0.20, then on a calculator, type this equation into it:

0.20 x 1.75 = 0.35

0.35 isn't the answer, but we use 0.35 to subtract it from 1.75:

1.75 - 0.35 = $1.40

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The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.

A square is a four sided polygon with 4 equal angles and length.

The fourth corner = 90° - 36°

= 54°

Recall,

Alternate angles are equal

So,

(4x + 4)° = 36°

substract 4 from both sides

4x = 36 - 4

4x = 32

divide both sides by 4

x = 32/4

x = 8

(4y + 10)° = 54°

substract 10 from both sides

4y = 54 - 10

4y = 44

divide both sides by 4

y = 44/4

y = 11

In conclusion, the value of the following given equations are:

(4x + 4)° = 36°

4(8) + 4 = 36

32 + 4 = 36

36° = 36°

(4y + 10)° = 54°

4(11) + 10 = 54

44 + 10 = 54

54 ^= 54°

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The answer can't be determined by the amount of data given in the question for ellipse.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

The standard equation for an ellipse is (x-h)²/a²+(y-k)²/b² = 1

a, b = semi-major and semi-minor axes respectively.

The center of the ellipse is at (0,0).

here, h=0, k=0.

One focus is at (12, 0)

Therefore

c = 12,

We can't find out the directrix with the given data.

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Roy's younger brother's age is 11 years.

According to the question,

We have the following information:

If Roy is 4 years older than his brother and the product of their ages is 165.

Now, let's take the age of Roy's younger brother to be x years.

Age of Roy = 4+x

So, we have the following expression:

x(4+x) = 165

[tex]x^{2} +4x-165=0[/tex]

Now, we will factorize this equation by splitting the middle term:

[tex]x^{2}[/tex]+15x-11x-165 = 0

Now, taking x as a common factor from the first two terms and -11 as a common factor from the last two terms:

x(x+15)-11(x+15) = 0

Taking (x+15) as a common factor:

(x+15) (x-11) = 0

x+15 = 0 and x-11 = 0

x = -15 and x = 11

Now, we know that age can not be negative.

Hence, Roy's younger brother is 11 years old.  

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Resolviendo una ecuación cuadratica encontraremos los catetos del triangulo, y con eso veremos que el area es:

A = 60.92m²

Para un triangulo rectangulo podemos definir:

Por el teorema de Pitagoras sabemos que:

x² + y² = h²

Y el area se escribe como:

A = x*y/2

Sabemos que:

x = h - 9m

x = y - 7m

Entonces:

h = x + 9m

y = x + 7m

Reemplazando eso en la ecuacion de Pitagoras:

x² + y² = h²

x² + (x + 7m)² = (x + 9m)²

x² + x² + 14m*x + 48m² = x² + 18m*x + 81m²

x² + x² - x² + 14m*x - 18m*x + 48m² - 81m² = 0

x² - 4m*x - 33m² = 0

las soluciones de la ecuación cuadratica son:

x = (4m ± √( (4m)² - 4*1*(-33m²))/(2)

x = (4m ± 12.16m)/2

Solo nos importa la solución positiva:

x = (4m + 12.16m)/2 = 8.08m

Entonces el otro cateto mide:

y = 8.08m + 7m = 15.08m

Y el area del triangulo será:

A = (8.08m)*(15.08m)/2 = 60.92m²

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The length of each of the other two pieces = 0.

Jessica cuts a ribbon with a length of 12 inches into three pieces.

The length of one piece is [tex]3\frac{1}{2}[/tex]

The lengths of the other two are the same

To find out the length of each of the other two pieces:

Based on the given conditions, we write formula as

(3-3)÷2

The sum of two opposites equals O: [tex]\frac{3-3}{2}[/tex]

Apply Zero property of Multiplication: 0

So we get the result = 0

Hence the answer if the length of each of the other two pieces = 0.

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The number of small boxes sent is 6 and the number of large boxes sent is 3.

Given:

Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books.

Let x be the number of small boxes and y be the number of large boxes.

20x + 35y = 225

x = 2y

20(2y) + 35y = 225

40y + 35y = 225

75y = 225

divide by 75 on both sides

75y/75 = 225/75

y = 225/75

y = 3 large boxes.

x = 2y

= 2*3

x= 6 small boxes.

Therefore the number of small boxes sent is 6 and the number of large boxes sent is 3.

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A stem club has 30 members and to find out how many ways are there to choose 4 members of the club to serve on an executive committee is as follows:

Given the stem club has 30 members.

The number of ways to choose 4 members of the club to serve on an executive committee is to be considered as 30c4

we know that the formula is

     [tex]n{cr}[/tex] = [tex]\frac{n!}{(n-r)!r!}[/tex]

there n = 30 and r = 4

that is., [tex]30_{c4}[/tex] = [tex]\frac{30!}{(30-4)!4!}[/tex]

                  = [tex]\frac{30!}{26!4!}[/tex]

                  = 29x15x7x9  = 27,405

Hence, the number of ways to choose 4 members of the club to serve on an executive committee is equal to 27,405.

Hence the number of ways to choose an executive member = 27,405

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No drew is incorrect and the right answer to this question is - 9/14 which can be calculated by using BODMAS rule.

What is BODMAS rule?

It stands for Bracket Of Division Multiplication Addition Subtraction which is a simple rule for solving calculation. It means first we solve brackets of a statement and so on.

Main Body:

Given :

⇒3/7÷ 2/3

This can be solved by changing the division to multiplication and taking reciprocal of the  term behind it.

⇒3/7×-3/2

⇒-9/14

Hence the correct answer to the statement is -9/14.

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Answer:

the rd one

Step-by-step explanation:

its the -21/2

if u need help tell me

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:

p-value = 0.09 is the probability of obtaining a value for the test statistic.

We are going step by step

Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample

Step 2) Here the Confidence level is equal to 0.95

So the level of significance is equal to 0.05

p-value = 0.09

Since the p-value is higher than the level of significance that we do not reject the null hypothesis.

Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.

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If there are 245 total preschoolers, there will be 105 boys.

acc to our question-

Therefore, there are 105 boys in the school.

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The value of x₃  , starting with  x₁ = 8 is 4.578

Given in the question ,

The iterative formula for the sequence is

=> xₙ₊₁ = 5 - 2 / xₙ

Also , x₁ = 8

Putting n = 2 in iterative formula

x₂ = 5 - 2 / x₁

Substituting the value of x₁

=> x₂ = 5 - 2 / 8

=> x₂ = 5 - 1 / 4

=> x₂ = (20 - 1)/4

=> x₂ = 19/4

=> x₂ = 4.75

Now , putting n = 3

x₃ = 5 - 2 / x₂

Substituting the value of x₂

=> x₃ = 5 - 2 / x₂

=> x₃ = 5 - 2 / 4.75

=> x₃ = 5 - 0.421

=> x₃ = 4.578

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Two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.

As given in the question,

Given set of numbers are :

{ 2,7,8,9}

Two digit prime numbers formed by given set of numbers are as follow:

When 2 and 8 are at unit place, number formed is a even composite number which is not prime.

Number formed when 7 at unit place are:

27, 87, 97 from which only 97 is prime.

Number formed when 9 at unit place are:

29, 79, 89 all three are prime numbers.

Therefore, two digit prime numbers formed by choosing two different digits from the given {2,7,8,9} set of numbers are 97, 29, 79, 89.

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Answer:

8x + 7

Step-by-step explanation:

5x + 3x = 8x

There are total 3027 chairs in the balcony and whole theater.

According to the Question,

There are total 325 rows, each rows have 09 chairs.

The number of chairs contains in theater are:

total number of rows × total chairs in rows

= 325 × 9 = 2925.

Again, there are additional 102 chairs in the balcony.

∴ 2925 + 102 = 3027

∴ There are total 3027 chairs in the whole theater.

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The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.

we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.

Here, the margin of error is E=2 and the level of significance is α=0.05

The critical value is Zα/2=Z₀.₀₂₅

or the critical value is 1.96

Now, we will find the sample size

n=((Zα/2)×σ/E)²

n=(1.96×8.4/2)²

n=67.76

n≈68

Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

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The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

In the question ,

seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.

we have to find statement which are true .

Option (a)

Thickness of the slide is dx for disk method and

dy for the shell method while rotating about x - axis ,

So , statement of option(a) is false .

Option(b)

In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,

thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,

So , statement of option (b) is false .

Option(c)

In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,

Thus , slices are cut perpendicular to the x axis .

statement of option (c) is True .

Option (d)

As in 2D , the  bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .

So , statement of option(d) is True .

Option(e)

When using shell method, we cut region into small slices perpendicular  to the x-axis .

So , statement of option(e) is False .

Option(f)

There can be both the kinds of cases , like in some cases disk method is easier than shell method and

in other cases shell method can be easier than disk method .

So , statement of option(f) is False .

Option(g)

When using disk method, we cut region into small slices perpendicular to x-axis .

So , statement of option (g) is False .

Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.

(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using shell method, we cut region into small slices parallel to x-axis.

The given question is incomplete , the complete question is

Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:

(a) The thickness of the slices will be dx for both methods.

(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.

(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.

(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.

(e) When using the shell method, we cut the region into small slices parallel to the x-axis.

(f) The shell method will always result in a less complicated integral.

(g) When using the disk method, we cut the region into small slices parallel to the z-axis.

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1) Exponential function to show the spread of Ben' s social media post is

y = 2(3)ˣ.

2) Exponential function to represent the spread of Carter's social media post is y = 10(2)ˣ.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When b > 0 and b 1, an exponential function has the form f(x) = bˣ. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

Given,

1) Exponential function to show the spread of Ben' s social media post:

y = 2(3)ˣ

2) Exponential function to represent the spread of Carter's social media post:

y = 10(2)ˣ

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Answer:

f(x) = –2x + 3

Step-by-step explanation:

The pressure applied on a cubic object with side 4inches with 50N force is 50N/m

Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area. The basic formula for pressure is F/A (Force per unit area). Unit of pressure is Pascals (Pa).

1 inch= 0.025m

4inches= 0.025×4= 0.1m

Pressure = Force/area

area= 0.1×0.1= 0.01m^2

therefore Pressure= 50/0.01

= 5000N/m^2

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The probability that both marbles drawn will be blue is 0.218.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Since there are 7 blue marbles in the bag.

The first blue marble drawing likelihood is 7/15.

The second blue stone has a 7/15 chance of being drawn.

The likelihood that both marbles are chosen will be blue is equal to 7/15*7/15,

= 49/225,

=0.218

Hence the probability of that both marbles drawn will be blue is =0.218

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Answer:

x > 2.8

Step-by-step explanation:

x < -x + 7(x - 2)

Expand using the Distributive Property

x < -x + 7x - 14

x < 6x - 14

Subtract x from both sides

0 < 6x - 14 - x

0 < 5x - 14

Add 14 for both sides

5x > 14

x > 14/5

x > 2.8

Answer:

(3, 1/64)

(−1, 4)

Step-by-step explanation:

took the test

Answer:

(3, 1/64)

(−1, 4)

Step-by-step explanation: toom the test :)

On a number line, plot the negative integers. The number that is further to the left will be less than the other.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

We have to explain how a number line can be used to compare two negative integers.

Integers are whole numbers they can be negative whole numbers or positive whole numbers for example 2, 4, 1, -8, 0, etc.

Plot the negative integers on a number line. It will be smaller than the other number if it is further to the left.

The numbers always go up (become "more positive") to the right and down (become "more negative") to the left on a number line. Numbers to the right are bigger than numbers to the left, and the opposite is true the other way around.

Thus, on a number line, plot the negative integers. The number that is further to the left will be less than the other.

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The true statements about the three quadrilateral is

The measurements of quadrilateral D  = 3 units and 1 units

The measurements of quadrilateral F = 3 units and 1 units

The measurements of quadrilateral E = 2 units and 6 units

The similar figure defined as the figures that have the same shape but not same size

The congruent is defined as the figures that have the same shape and size

Here D and F are congruent but they are not similar because they have same size

D and E are similar but not congruent because of same shape and different size.

Hence, true statements about the three quadrilateral is

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If the triangle is equiangular, then the triangle is an equilateral triangle.

What is equiangular triangle?

A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60

What is equilateral triangle?

an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°.

As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.

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