Amy sold 10 packages of sugar cookies and 2 packages of oatmeal
cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of
oatmeal cookies for $60. What is the price of a pack of sugar cookies and a
pack of oatmeal cookies?

Given:

∠1 = 2x+6 ans ∠2= -x+24

To find the values of ∠1 and ∠2.

Formula:

The values of the vertical angles are always equal.

Here,

∠1 and ∠2 are vertical angles.

So, by this condition,

∠1=∠2

or,[tex]2x+6 = -x+24[/tex]

or, [tex]2x+x = 24-6[/tex] [ Taking all the variables in one side and all the constant in other side]

or, [tex]3x = 18\\[/tex]

or, [tex]x = \frac{18}{3}[/tex]

or, [tex]x = 6[/tex]

So,

∠1 = [tex]2(6)+6 = 18^\circ[/tex]

∠2 =[tex]-6+24 = 18^\circ[/tex]

Hence,

The values of ∠1 and ∠2 are 18°.

Answer:

B

Step-by-step explanation:

[tex]\frac{3.683 \times 10^4}{7.51 \times 10^{12}} \\=\frac{36.83 \times 10^3}{7.51 \times 10^{12}} \\=\frac{36.83}{7.51} \times 10^{3-12}\\ \approx 4.9041 \times 10^{-9}[/tex]

The quotient in the scientific notation form will be 4.9041 × 10⁻⁹. The correct option is B.

Scientific notation can be used to indicate numbers that are either too big or too little to be conveniently stated in decimal form. It may be called scientific form.

Standard notation is the practice of writing a number using nothing but its digits. This is how numbers are usually expressed because traditional number notation does not utilize words.

Given that the two numbers are (3.683 × 10⁴) and (7.51 × 10¹²). The quotient will be calculated as:-

Quotient = (3.683 × 10⁴) ÷ (7.51 × 10¹²)

Quotient = 0.49 x 10⁻⁸

Quotient = 4.9 x 10⁻⁹

The quotient will be 4.9041 × 10⁻⁹.

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Answer:

A.) [tex]3-3\log _{10}\left(30\right)[/tex] or -1.43136... (Decimal Form)

B.) [tex]\log _6\left(2\right)+2\log _6\left(w\right)[/tex]

Explanation: I inserted image to explain how to solve the second one, but for the first one you can't go any further except writing it in standard form or changing it into a decimal.

Your welcome :3

Answer: The probability that a randomly selected teacher will make more than $40,542 per year is 0.82

Step-by-step explanation:

Looking at the information given, the population mean and population standard deviation are known. We would apply the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = $42335

σ = 2000

x = $40542

The probability that a randomly selected teacher will make more than $40,542 per year is expressed as

P(x > 40542) = 1 - P(x ≤ 40542)

For P(x ≤ 40542),

z = (40542 - 42335)/2000 = - 0.9

Looking at the normal distribution table, the probability corresponding to the z score is 0.18

P(x > 40542) = 1 - 0.18 = 0.82

Answer:

62.1

Step-by-step explanation:

90 percent means there are 90 parts from all 100 parts

90/100 × 69 = 62.1

Answer:

62.1

Step-by-step explanation:

I dont really have an explanation. sorry :(

Joni should have multiplied by 1,000.

Step-by-step explanation:

Mass of the box = 67 decagrams

1 decagram = 1000 centigrams

So, 67 decagrams = 67 x 1000 centigrams

= 67000 centigrams

Joni should have multiplied by 1,000.

Answer:

its A

Step-by-step explanation:

got it right on EDG

Answer:

$2.52/12= $.21

the cost of one can of soda is $.21

Step-by-step explanation:

Answer:

$0.21 per can.

Step-by-step explanation:

You divide the amount of money for all 12 cans by 12.

2.52/12=0.21

Answer:

divide and 12

42

Step-by-step explanation:

Hope it helps!

Answer:

divide by 12!

Step-by-step explanation:

to convert inches to feet you divide by 12. to convert feet to inches you multiply by 12

Answer:

B.

Step-by-step explanation:

It just is...i got it right

Answer: 67.

Step-by-step explanation: To find the range of a set of numbers, all you have to do is subtract the smallest number in the set from the largest number. In this case, the smallest number would be 7 and the largest number would be 74. 74 - 7 equals 67, and so the range is 67.

Final answer:

The range is the difference between the largest and smallest numbers in the set. For the numbers 66, 8, 12, 74, 36, 66, 7, the range is 67.

Explanation:

The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 66, 8, 12, 74, 36, 66, 7, you would first identify the smallest and largest number, which are 7 and 74, respectively. Then, subtract the smallest number from the largest number: 74 - 7 = 67.

Therefore, the range of the set of numbers is 67.

Answer:

300

Step-by-step explanation:

if Elizabeth tagged 75 and observes 260 with 25 already taged yo need to add 260+75-25+310

since you need to round to nearest whole number it will be 300

I believe that is is 300

Answer:

8 and 6

Step-by-step explanation:

8 * 6 = 48

8 + 6 = 14

Answer:

Step-by-step explanation:

Given that A university has 28,470 students.

In a random sample of 285 students, 19 speak three or more languages.

From the given 19 out of 285 speaks three or more languages, a expected number of students would be given by

[tex]28470\times (\frac{19}{285})[/tex]

[tex]=\frac{540930}{285}[/tex]

[tex]=1898[/tex]

84 of 300 is 252.

84% × 300 =

84 ÷ 100 × 300 =

84 × 300 ÷ 100 =

25200 ÷ 100 =

252

Answer:

CHALLENGE ACCEPTED!

Step-by-step explanation:

15420 + 38N + 836 = -33N - 1122

15420 + 836 + 1122 = -333N -38N

17378 = -371N

N = -46.8

Answer:

11 ft by 5.5 ft

Step-by-step explanation:

The scale is 2in for 2 ft or 1in for 1ft

This means that you can just take the number in inches and change it to feet. Therefore 11 inches turns to 11 feet and 5.5 inches turns into 5.5 feet.

Answer:

C: Linear model

Step-by-step explanation:

Answer:

20, 40, and 120

Step-by-step explanation:

x, 2x, and 6x have one thing in common: X. X is the same number throughout so if we find x we can just finish the equation by multiplying x by its coefficient.

x+2x+6x = 180. (Sum of angle measures)

9x           = 180 (Add up the left side)

9x/9        = 180/9 (Divide both sides by 9 to cancel out the 9 and leave the x)

x              = 20

Now we know what x is so:

Angle 1 = 20. (We know x is 20, so that one is easy.)

Angle 2 = 40 (Simply 2*x or 2*20)

Angle 3 = 120 (Simply 6*x or 6*20)

Answer:

Step-by-step explanation:

24 i think so

u use sin and just do sin(x)=29/34 and then use inverse sin

Answer:

(a) 45 miles

(b) 38 miles

(c) Jada travels faster than Andre.

Step-by-step explanation:

(a) First we calculate the speed at which Jada travelled:

[tex]Speed = \frac{distance}{time} \\\\\\s = \frac{d}{t}[/tex]

[tex]s = \frac{135}{3} \\\\\\s = 45 miles/hour[/tex]

Since Jada travels at constant speed throughout the journey, we can calculate the distance traveled in 1 hour:

[tex]distance = speed * time\\\\\\distance = 45 * 1[/tex]

distance = 45 miles

Jada travels 45 miles in 1 hour.

(b) We calculate the speed at which Andre travelled:

[tex]Speed = \frac{distance}{time} \\\\\\s = \frac{d}{t}[/tex]

[tex]s = \frac{228}{6} \\\\\\s = 38 miles/hour[/tex]

Since Andre travels at constant speed throughout the journey, we can calculate the distance traveled in 1 hour:

[tex]distance = speed * time\\\\\\distance = 38 * 1[/tex]

distance = 38 miles

Andre travels 38 miles in 1 hour.

(c) Jada travels faster than Andre because he has a higher speed (45 miles/hour) than Andre ( 38 miles/hour).

To multiply monomials, you multiply the coefficients and add the exponents of like variables. The product of -9n^3 and n^3 is -9n^6.

The question is about multiplying two monomials in mathematics. In this case, the two monomials are -9n^3 and n^3. To multiply monomials, you multiply the numerical coefficients and add the exponents of like variables. Here, the coefficient is -9 and the exponent 3 for the first monomial and 1 and 3 for the second monomial. When you multiply -9 by 1, you get -9. When you add the exponents 3 and 3, you get 6. So, the product of those two monomials in standard form is -9n^6.

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Answer:

  ln(2) +3ln(a) -4ln(b)

Step-by-step explanation:

  [tex]\ln{\left(\dfrac{2a^3}{b^4}\right)}=\ln{(2a^3b^{-4})}=\ln{(2)}+\ln{(a^3)}+\ln{(b^{-4})}\\\\=\boxed{\ln{(2)}+3\ln{(a)}-4\ln{(b)}}[/tex]

__

The applicable rules of logarithms are ...

  log(ab) = log(a)+log(b)

  log(a^b) = b·log(a)

Final answer:

To expand the expression In 2a³/b⁴, you apply logarithm properties to obtain In 2 + 3 In a - 4 In b, which separates the factors into individual log terms.

Explanation:

The question asks us to expand the logarithmic expression In 2a³/b⁴ using logarithm properties. The correct expansion of this expression is given by the sum of the logarithms of the numerator's factors minus the sum of the logarithms of the denominator's factors. Applying the properties of logarithms (product to sum and quotient to difference), we obtain the expansion as follows:

In 2a³/b⁴ = In 2 + In a³ - In b⁴

The logarithm of a power (such as In a³ and In b⁴) can be brought down as a coefficient:

In 2 + 3 In a - 4 In b

Thus, the correct expansion is In 2 + 3 In a - 4 In b.

Answer:

Nathan

Step-by-step explanation:

Because 4.76 ÷ 2.5 is 1.904

Nathan is correct about the decimal being misplaced in the quotient. The correct division of 4.76 by 2.5 should give 1.904 when rounded off to two decimal places.

In this case, Nathan is correct in stating that the decimal is misplaced in the quotient. When rounding to two decimal places, the correct calculation should be 4.76 ÷ 2.5 = 1.904, not 0.19. The decimal point division process can be simplified as follows:

Another approach would be to simply use a calculator to confirm the correct division of 4.76 by 2.5.

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Answer:

26.25

Step-by-step explanation:

Answer:

Your're answer is 84.

Answer:

1/30 = 3.33%

Step-by-step explanation:

There are 3 different flavors available and the favorable outcome is only strawberry flavor. There are 10 toppings and the favorable outcome is sprinkle. To calculate the probability for the two events, you just need to multiply both. The calculation will be:

P(strawberry) * P(sprinkle) = 1/3 * 1/10= 1/30

The probability of the next customer ordering strawberry ice cream with sprinkles, given that there are 3 flavors and 10 toppings, is 1/30.

The student asks about the probability of a specific ice cream order at an ice cream shop, which involves both flavor selection and topping selection. Since there are 3 different flavors and 10 different toppings, we treat these choices as independent events. The probability of selecting strawberry ice cream is 1/3, as it is one of the three available flavors. The probability of selecting sprinkles as a topping is 1/10, since it is one of ten toppings. To find the total probability of both events occurring (strawberry ice cream with sprinkles), we multiply the two separate probabilities:

Probability = Probability of strawberry ice cream times Probability of sprinkles = 1/3 times 1/10 = 1/30.