In triangle XYZ, the measure of angle Z is 42°, and the measure of angle Y is 68.4°. What is the measure of angle X?

Answer:

c

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

\(\Huge \boxed{\bold{\text{12 Boys}}}\)

\(\Huge \boxed{\bold{\text{30 Girls}}}\)

Step-by-step explanation:

Let the number of girls be \(g\) and the number of boys be \(b\).

According to the problem: \(b = \frac{2}{5} \times g\)

We also know that the total number of students is 42, so \(b + g = 42\).

Now, we have two equations with two variables:

We can solve these equations to find the values of \(b\) and \(g\).

Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)

From the first equation, we have\(b = \frac{2}{5} \times g\)

Step 2: Substitute the expression for \(\bold{b}\) into the second equation

Replace \(b\) in the second equation with the expression we found in step 1.

\(\frac{2}{5} \times g + g = 42\)

Step 3: Solve for \(\bold{g}\)

Now, we have an equation with only one variable, \(g\):

\(\frac{2}{5} \times g + g = 42\)

To solve for \(g\), first find a common denominator for the fractions:

\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)

Combine the fractions:

\(\frac{7}{5} \times g = 42\)

Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):

Step 4: Find the value of \(\bold{b}\)

Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:

So, there are 12 boys and 30 girls in the class.

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1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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Answer:

4103.7 is the answer

I HOPE IT IS HELPFUL

Answer: Sir in what way would you like me to explain this

Step-by-step explanation:

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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I will assume the general table given in the problem.

-------------------------------------------------------------------------------------

Let's draw the table,

Since all the information and total is given, except physics, let us calculate the two blanks in the table.

So, the completed table is,

We want the probability of selecting a female student taking physics.

For that, we need the number of female physics students and the total number of students.

From the table, we see that,

Female Physics students = 45

Total number of students = 175 + 175 = 350

Thus,

The probability of selecting a female student taking physics is 45/350

Or,

0.12857

Rounding to the nearest hundredth (2 decimal places), the answer is

0.13

Answer:

Step-by-step explanation:

As per properties mentioned above we have:

ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°

Side opposite to 30 is half of the length of the hypotenuse

AD is opposite to ∠B and BD is the hypotenuse, then:

and

Answer:

The answer is 0 I'm pretty sure

Step-by-step explanation:

Answer:

\(x=-\frac{5}{4}\pm\frac{\sqrt{89}}{4}\)

Step-by-step explanation:

\(-2x^2-5x+25=17\\-2x^2-5x+8=0\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-5)\pm\sqrt{(-5)^2-4(-2)(8)}}{2(-2)}\\x=\frac{5\pm\sqrt{25+64}}{-4}\\x=\frac{5\pm\sqrt{89}}{-4}\\x=-\frac{5}{4}\pm\frac{\sqrt{89}}{4}\\\)

9514 1404 393

Answer:

Step-by-step explanation:

The ratio of smallest sides in the two triangles is ...

  smaller / larger = 4/10

To find A and B, we write proportions involving corresponding side lengths.

__

Side A in the smaller triangle is ...

  A/15 = 4/10

  A = (4/10)(15) = 6

__

The ratio of larger to smaller is the inverse of the above ratio, so ...

  B/9 = 10/4

  B = (10/4)(9) = 22.5

The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:

B = V/6.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:

B = V/6.

The table is given by the image presented at the end of the answer.

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Answer:

a) .38 × 2,450 = 931 people buy the local newspaper.

b) 2,450 - 931 = 1,519 people do not buy the local newspaper.

Answer:

16 and 9

Step-by-step explanation:

16 × 19 using the distributive property

16 × 10 + 16 × 9

Answer:

\(f(x) = x + 4\)

Step-by-step explanation:

\(y - 8 = x - 4\)

Add 8 to both sides to isolate the y

\(y = x - 4 + 8\)

then you're left with y = x + 4

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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A=a+b/2×h=5+10/2×4=30. this might helpful

Answer:

is it twelve ?

Step-by-step explanation:

:-|

Answer:

c. 92,598

Step-by-step explanation:

20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08

= 92597.

= 92,598

The negations of the given statements with the application of De Morgan's law and/or conditional law.

a) ∃x (¬P(x) ∨ ¬R(x))

De Morgan's law:

∃y ∀z(¬P(y) ∧ ¬Q(z))

b) ∃y ∀z(¬P(y) ∧ ¬Q(z))

The double negation:

∃y ¬∃z(P(y) ∨ Q(z))

c) ¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

The conditional law:

¬∃x (P(x) ∨ (∀z (¬R(z)) → (∀z ¬Q(z))))

Let's form the negation of the given statements and apply De Morgan's law and/or conditional law, when applicable:

a) ∀x (P(x) ∧ R(x))

The negation of this statement is:

∃x ¬(P(x) ∧ R(x))

Now let's apply De Morgan's law:

∃x (¬P(x) ∨ ¬R(x))

b) ∀y∃z(¬P(y) → Q(z))

The negation of this statement is:

∃y ¬∃z(¬P(y) → Q(z))

Using the conditional law, we can rewrite the negation as:

∃y ¬∃z(¬¬P(y) ∨ Q(z))

c) ∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

The negation of this statement is:

¬∃x (P(x) ∨ (∀z (¬R(z) → ¬Q(z))))

Using the conditional law, we can rewrite the negation as:

¬∃x (P(x) ∨ (∀z (R(z) ∨ ¬Q(z))))

Applying De Morgan's law:

¬∃x (P(x) ∨ (∀z ¬(¬R(z) ∧ Q(z))))

Simplifying the double negation:

¬∃x (P(x) ∨ (∀z ¬(R(z) ∧ Q(z))))

Using De Morgan's law again:

¬∃x (P(x) ∨ (∀z (¬R(z) ∨ ¬Q(z))))

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Answer:

Mark's mass is 26 kg.

Step-by-step explanation:

Average mass of Jeremy, Mark and Zack = 28kg

Average mass of Jeremy and Zack = 29 kg

Let,

Jeremy's mass = x

Mark's mass = y

Zack's mass = z

Average of three of them = \(\frac{Jeremy's mass + Mark's + Zack's}{3}\)

28 = \(\frac{x+y+z}{3}\\\)

\(28*3 = x+y+z\\84 = x+y+z\)

x+y+z = 84     Eqn 1

\(29 =\frac{x+z}{2}\\58=x+z\\\)

x+z = 58    Eqn 2

Now putting value of x+z from Eqn 2 in Eqn 1

x + z + y = 84

58 + y = 84

y = 84 - 58

y = 26

Thereofore,

Mark's mass is 26 kg.

Answer:

(3)

Distance the train can travel=252km

Distance the train can travel in 1 hour=252÷42=6km

The time needed to cover 350km= 350÷6=58.4 hours.

(4)

The cost of 1 articles=$1.95

The cost of 15 articles= 15(1.95)=$29.25

(5)

Cost of 25 articles= 43.75

Cost of 1 article= 43.75/25=1.75

(6)

Liters of petrol needed when a car travels 240km=20litre

liters of petrol needed when a car travels 600km= 20/240 x600

20/24x60

20/4x10

5x10=50liter

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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The given statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants." is true.

The term probability refers the occurrence of a random event.

Here we have given the statement "A two-factor study compares 2 levels of factor A and 3 levels of factor B with a sample of n = 5 participants in each treatment condition. This study uses a total of 25 participants."

And we have to identify whether this one is true or not.

While looking into the given question, we have identified the value like the following,

level in factor A = 2

levels in factor B = 3

Number of participants = 5

Then the total number of participants is calculated as,

=> (3 + 2)  x 5

Now, we have to expand the given equation, then we get,

=> 5 x 5

Then the total number of participants is 25.

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Adjacent = 12

Explanation:

The shape is a right angled triangle

Using pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse is the longest side = 13

opposite is the vertical side or the side opposite the angle = 5

Adjacent is the base. it is not given in the question.

So we need to find it.

using the formula:

13² = 5² + adjacent²

169 = 25 + adjacent²

collect like terms:

169 - 25 = adjacent²

144 = adjacent²

square root both sides:

√144 = √( adjacent²)

12 = adjacent

Adjacent = 12

Hence, the value missing side is 12

The bottle that holds more water has the larger volume

Beau's water bottle holds more water

The given parameters are:

Drew

Beau

The volumes of their bottles is calculated using:

V = πr^2h

So, we have:

Drew = 3.14 * (3/2)^2 * 7

Drew = 49.46

Beau = 3.14 * (2)^2 * 9

Beau = 113.04

By comparison, 113.04 is greater than 49.46

Hence, Beau's water bottle holds more water

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Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Answer:

\(\fbox {77}\)

Step-by-step explanation:

Given

⇒ a = 5

⇒ d = + 8

Solving :

⇒ a₁₀ = a + 9d

⇒ a₁₀ = 5 + 9(8)

⇒ a₁₀ = 5 + 72

⇒ a₁₀ = 77