To win a trivia game, Nathan must score at least 105 points. Each correct answer is worth \large 3\frac{1}{3} points, and each incorrect answer is worth \large -\frac{1}{2} . If he gets 33 questions correct and 20 questions incorrect, how many points does he have? Does he win? (yes or no)

Answer:

Step-by-step explanation:

Let the number TJ thinks of be n.

If he finds 1/3 of the number, the expression that models this situation is expressed as:

1/3 of n

= 1/3 * n

= n/3

hence the expression that models the scenario is n/3

Answer:

1/3n-5

Step-by-step explanation:

Answer:

7/8 is the simplified fraction for 56/64 by using the GCD or HCF method. Thus, 7/8 is the simplified fraction for 56/64 by using the prime factorization method.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

10 times 10 equals 100

Answer:

A. 0.9510

B. 0.0480

C. 0.0490

D. No, I would not feel comfortable accepting the shipment if one item was found defective, because the probability is quite small to obtain 1 or more defective items.

Answer:

0.09

Step-by-step explanation:

First off, we can write 0.9 as a fraction. Reading this, we would say "nine tenths"; this means the number in fraction form is 9/10.

The word "of" in mathematics means we multiply. Thus when we take 1/10 "of" 9/10, we multiply the two:

1/10(9/10)

To multiply fractions, multiply the numerators and multiply the denominators:

1/10(9/10) = (1*9)/(10*10) = 9/100

Converting this back to a decimal, we read 9/100 as "nine one-hundredths"; this means decimal form is 0.09.

Answer:

80 miles per hour

Step-by-step explanation:

To find her speed in miles per hour, multiply 20 by 4.

Since she drove 20 miles in 1/4 of an hour, we can find the amount she can drive in 1 full hour by multiplying it by 4.

20(4)

= 80

So, her rate in miles per hour is 80 miles per hour

Answer:

80 mph

Step-by-step explanation:

20 miles multiplied by 4(quarters of the hour) is 80mph

Answer: 496

Step-by-step explanation:

Answer:

Therefore, the correct option is: Its value is 1/10 the value of the underlined digit.

Note: The question is incomplete. The complete question is given below:

2. In the number shown, one digit is underlined and one digit is circled. Which statement about the circled digit is true?

Its value is 10 times greater than the value of the underlined digit.

Its value is 1/10 the value of the underlined digit.

Its value is 70 times the value of the underlined digit.

Its value is 1/70 the value of the underlined digit.

See attachment below for the number

Step-by-step explanation:

This problem is about the place value of whole numbers.

Step 1: Determining the place value of the numbers

The place value is the value of each digit in a number, be it a whole number or a decimal number.

The number shown is seventy seven thousand (77,000)

The place value of the underlined 7 is 7 ten thousands = 7 * 10000 = 70000

The place value of the circled 7 is 7 thousands = 7 * 1000 = 7000

Step 2: Comparing the numbers

Comparing the circled number and the underlined number:

7000/70000 = 1/10

Therefore, the correct option is: Its value is 1/10 the value of the underlined digit.

Answer:

1=4 being the co interior angle

2=3 being the opposite angle

Answer:

The slope of the line is two.

Step-by-step explanation:

Recall that to find the slope between any two points, we can use the slope formula:

[tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Let (6, 8) be our (x₁, y₁) and let (1, -2) be our (x₂, y₂). Substitution yields:

[tex]\displaystyle m=\frac{(-2)-(8)}{(1)-(6)}[/tex]

Subtract:

[tex]\displaystyle m=\frac{-10}{-5}[/tex]

Divide:

[tex]m=2[/tex]

Therefore, the slope of the line is two.

Answer:

2

Step-by-step explanation:

Answer:

The function in the vertex form is y = (x + 2.5)² - 15.25

Step-by-step explanation:

The vertex form of the quadratic function y = ax² + bx + c is:

y = a(x - h)² + k, where

∵ The given function is y = x² + 5x - 9

∴ a = 1, b = 5, c = -9

→ Use a and b to find h

∵ h = [tex]\frac{-b}{2a}[/tex]

∴ h = [tex]\frac{-5}{2(1)}=-2.5[/tex]

∴ h = -2.5

→ Find y at x = -2.5

∵ y = (-2.5)² + 5(-2.5) - 9 = 6.25 - 12.5 - 9

∴ y = -15.25

∴ k = -15.25

→ Substitute a, h, k in the vertex form above

∴ y = 1(x - -2.5)² + -15.25

∴ y = (x + 2.5)² - 15.25

The function in the vertex form is y = (x + 2.5)² - 15.25

Subtract the amount she gives her mom from the total amount she has:

22 - 12 = 10

She has 10 boxes left.

I think it's A :)))

..........

Answer:

Step-by-step explanation:

See the attached picture for a drawing of the angle and its terminal point coordinates. Those are (cos(4π/3), sin(4π/3)), so we have the following trig function values:

  sin(4π/3) = -√3/2

  cos(4π/3) = -1/2

  tan(4π/3) = sin/cos = √3

  sec(4π/3) = 1/cos = -2

  csc(4π/3) = 1/sin = -(2√3)/3

  cot(4π/3) = 1/tan = (√3)/3

_____

Additional comment

It helps to know that 1/√a = (√a)/a. This lets you write the ratios with a rational denominator in each case.

Answer:

1.0

Step-by-step explanation:

you have to follow the arrow

Answer:

2 mm

Step-by-step explanation:

let the radius of the semi-circle be r

Then,

length of curved portion = 1/2 x circumference = (1/2) (2)(π)r = πr

length of straight portion = diameter of circle = 2r

Hence, we can write an expression for the perimeter

Perimeter = length of curved portion + length of straight portion

Perimeter = πr + 2r

Perimeter = (π + 2)r

since we are given the perimeter = 5.14, assuming that π=3.14, our equation becomes:

5.14 = (3.14 + 2)r

5.14 = 5.14 r

r = 5.14 / 5.14 = 1

Hence, diameter = 2r = 2(1) = 2 mm

A: How many total hours were worked this week?

Answer- 14 hours were worked this week

B: How many overtime hours were worked?

Answer- 36 overtime hours were worked

I hope this helps you out!!

Answer:

A. 41 hours were worked the whole week

Answer:

x < -5

Step-by-step explanation:

first you do 12 - 7 which equals to 5

and then put x < becuase -12 is less than -7

Answer:g

Step-by-step explanation:

//////l??///??????/////

Answer:

Yes.

Step-by-step explanation:

[tex]6^{3}[/tex] × [tex]7^{3}[/tex] = [tex]42^{3}[/tex]

74,088 = 74,088

Answer:

P(≥ 7 males) = 0.0548

Step-by-step explanation:

This is a binomial probability distribution problem.

We are told that Before 1918;

P(male) = 40% = 0.4

P(female) = 60% = 0.6

n = 10

Thus;probability that 7 or more were male is;

P(≥ 7 males) = P(7) + P(8) + P(9) + P(10)

Now, binomial probability formula is;

P(x) = [n!/((n - x)! × x!)] × p^(x) × q^(n - x)

Now, p = 0.4 and q = 0.6.

Also, n = 10

Thus;

P(7) = [10!/((10 - 7)! × 7!)] × 0.4^(7) × 0.6^(10 - 7)

P(7) = 0.0425

P(8) = [10!/((10 - 8)! × 8!)] × 0.4^(8) × 0.6^(10 - 8)

P(8) = 0.0106

P(9) = [10!/((10 - 9)! × 9!)] × 0.4^(9) × 0.6^(10 - 9)

P(9) = 0.0016

P(10) = [10!/((10 - 10)! × 10!)] × 0.4^(10) × 0.6^(10 - 10)

P(10) = 0.0001

Thus;

P(≥ 7 males) = 0.0425 + 0.0106 + 0.0016 + 0.0001 = 0.0548

Answer:

x-intercept (-7.5, 0)

y-intercept (0, 5.5)

Hope this helps!

Answer:

g(x) = x + 3

Step-by-step explanation:

A composite function is a function that is written inside another function which means substituting one function into another function.

Ex: (fоg)(x) is a composite function, where x of f(x) is substituted by g(x)

∵ h(x) = (fоg)(x)

∵ [tex]h(x)=\sqrt{x+5}[/tex]

∵ [tex]f(x)=\sqrt{x+2}[/tex]

→ Substitute x of f(x) by g(x)

∴  (fоg)(x) = [tex]\sqrt{g(x)+2}[/tex]

→ Equate (fоg)(x) by h(x)

∴ [tex]\sqrt{g(x)+2}=\sqrt{x+5}[/tex]

→ Cancel the roots from the two sides

∴ g(x) + 2 = x + 5

→ Subtract 2 from both sides

∴ g(x) + 2 - 2 = x + 5  - 2

∴ g(x) = x + 3