A. Grace spent P184.35 for a box of chocolates and
handkerchiefs. She gave her sister P125.00. The money she had left was
P127.75? How much did she have at first?
1. What is asked in the problem?
2. What are the given facts?
3. What is the operation to be used?
4. What is the number sentence?
5. What is the solution?​

Answer:

The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

12% of the employees wear contact lenses.

This means that [tex]p = 0.12[/tex]

Samples of 500:

This means that [tex]n = 500[/tex]

What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses?

Mean:

[tex]\mu = p = 0.12[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{500}} = 0.0145[/tex]

The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.

Answer:

[tex]t = 4b + 10c[/tex]

Step-by-step explanation:

Given

1 bag = 4 doughnuts

1 carton = 10 doughnuts

Required

Determine the amount of doughnuts in b bags and c cartons

If 1 bag contains 4 doughnuts, then b bags contain 4b doughnuts

If 1 carton contains 10 doughnuts, then c cartons contain 10b doughnuts

So, the total (t) is calculated by adding up the amount of doughnuts in the cartons and the bags:

i.e.

[tex]t = 4b + 10c[/tex]

Answer:

[tex]Area = 65.94[/tex]

Step-by-step explanation:

I will assume that the shaded region is the fire pit

Given

[tex]R = 5[/tex]

[tex]r = 2[/tex]

Required

Determine the area of the fire pit

First, calculate the area of the big circle.

[tex]A_2 = \pi R^2[/tex]

Area of the small is:

[tex]A_1 = \pi r^2[/tex]

The area of the pit is:

[tex]Area = A_2 - A_1[/tex]

[tex]Area = \pi R^2 - \pi r^2[/tex]

[tex]Area = \pi (R^2 - r^2)[/tex]

[tex]Area = 3.14 (5^2 - 2^2)[/tex]

[tex]Area = 3.14 (25 - 4)[/tex]

[tex]Area = 3.14 * 21[/tex]

[tex]Area = 65.94[/tex]

Answer:

-48.4328358209

Step-by-step explanation:

hope this helps!!!

Answer:

If you meant 68-67 then it would be 1288

But if you meant 67-68 it is -1288

(I really hope this isn't hard to understand).

Given:

The two ratios are 13:15 and 30:26.

To find:

Whether the given ratios are equivalent or not.

Solution:

Two ratios are equivalent if the values of the ratio are equal after simplification.

[tex]13:15=\dfrac{13}{15}[/tex]

And,

[tex]30:26=\dfrac{30}{26}[/tex]

[tex]30:26=\dfrac{15}{13}[/tex]

[tex]30:26=15:13[/tex]

The first ratio is 13:15 and the value of second ratio after simplification is 15:13 both ratios are different, so,

[tex]\dfrac{13}{15}\neq \dfrac{30}{26}[/tex]

Therefore, the required answer is "No", the given ratios are not a pair of equivalent ratios.

multiplication of the gradients of the two diagonals is equals to -1 if they are perpendicular

Answer:

729

Step-by-step explanation:

Answer:

120.4ft

Step-by-step explanation:

Find the diagram in the attachment.

The triangle shown is a right angled triangle with the side DE as the hypotenuse, EF is adjacent side while DF is the opposite side.

To get DE, we will use the SOH CAH TOA trigonometry identity

Using CAH which is defined as:

Cos(theta) = Adjacent/Hypotenuse

Cos 79°= 23/Hypotenuse

Hypotenuse = 23/cos79°

Hypotenuse = 23/0.191

Hypotenuse = 120.4feet

DE = 120.4feet (to nearest tenth)

The required difference in the expression (f – g)(x) is - 6x³+ 4x² + 4x - 8

Given the following functions

f(x) = 2x² + 4x - 5

g(x) = 6x³ – 2x² + 3

In order to get the required function (f-g)(x), we will have to take the difference of the function as shown:

(f – g)(x) = f(x) - g(x)

Substitute the given parameters into the expression

(f – g)(x) = 2x² + 4x - 5 - (6x³ – 2x² + 3)

Expand

(f – g)(x) = 2x² + 4x - 5 - 6x³ + 2x² - 3

Collect the like terms

(f – g)(x) = 2x²+2x²- 6x³ + 4x -5 -3

(f – g)(x) = - 6x³+ 4x² + 4x -5 -3

(f – g)(x) =  - 6x³+ 4x² + 4x - 8

Hence the required difference in the expression (f – g)(x) is - 6x³+ 4x² + 4x - 8

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Answer:11.39

Step-by-step explanation:

Answer:

(0,-4)

Step-by-step explanation:

Given

[tex]f(x) = x^\frac{1}{3} - 4[/tex]

Required

Determine the critical numbers

[tex]f(x) = x^\frac{1}{3} - 4[/tex]

Differentiate:

[tex]f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}[/tex]

[tex]f'(x) = \frac{1}{3}x^{-\frac{2}{3}}[/tex]

Equate to 0

[tex]f'(x) = \frac{1}{3}x^{-\frac{2}{3}} = 0[/tex]

[tex]\frac{1}{3}x^{-\frac{2}{3}} = 0[/tex]

Multiply through by 3

[tex]3 * \frac{1}{3}x^{-\frac{2}{3}} = 0*3[/tex]

[tex]x^{-\frac{2}{3}} = 0[/tex]

[tex]x = 0[/tex]

Substitute 0 for x in [tex]f(x) = x^\frac{1}{3} - 4[/tex]

[tex]f(0) = 0^\frac{1}{3} - 4[/tex]

[tex]f(0) = 0- 4[/tex]

[tex]f(0) = - 4[/tex]

Hence, the critical point is: (0,-4)

Answer:

what was the question I dont get it pls

Step-by-step explanation:

u can tell me

Answer:

[tex]\displaystyle d = 4\sqrt{5}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-5, 6) → x₁ = -5, y₁ = 6

Point (3, 2) → x₂ = 3, y₂ = 2

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

ella tiene que pagar 10 por mes. lo siento si no es así, esa no es la respuesta correcta.

Step-by-step explanation:

Answer:

Angle DCA = Angle CAB. (Alternate Interior Angle)

Angle DCA = 68°

Angles(DCA + ACB + BCE) = 180°. (Linear Pair)

Angle ACB + 68° + 33° = 180°

Angle ACB = 79°

Therefore,

Angle ABC = 33°. (Alternate Interior Angle)

Answer:

83.4

Step-by-step explanation:

16.2 x 2

=

32.4 +

1/2 x 8.5 x 12  

=

51 + 32.4 = 83.4

Hope this helps!

Answer:

$12,000.

Step-by-step explanation:

Given that in the year 2001, a person bought a new car for $ 15500, and for each consecutive year after that, the value of the car depreciated by 5%, to determine how much would the car be worth in the year 2005, to the nearest hundred dollars, the following calculation must be performed:

100-5 = 95

15,500 x 0.95 x 0.95 x 0.95 x 0.95 x 0.95 = X

14.725 x 0.95 x 0.95 x 0.95 x 0.95 = X

13,988.75 x 0.95 x 0.95 x 0.95 = X

13,289.3125 x 0.95 x 0.95 = X

12,624.846875 x 0.95 = X

11.993.60453125 = X

Thus, to the nearest hundred dollars, the cost of the car after 5 years will be $ 12,000.

Answer:

5.5n -2 -0.5p

Step-by-step explanation:

Make Everything to either decimals or fractions.

then simplify as shown

Answer:

3/4

Step-by-step explanation:

The value of tangent ratio [tex]tan \beta[/tex] in the triangle is [tex]\frac{3}{4}[/tex].

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Review all six trigonometric ratios: sine, cosine, tangent, cotangent, secant, & cosecant.

Tangent ratio is yet another trigonometric ratio for right-angled triangles. Tangent ratio is the ratio of opposite side to adjacent side of a right triangle.

According to the triangle ABC

<C = [tex]90^{0}[/tex], <B = [tex]\beta[/tex], AB = 5, BC = 4, AC = 3

Tangent ratio is the ratio of opposite side to adjacent side of a right triangle.

Tangent ratio is one of the trigonometric ratios.

[tex]tan \beta=\frac{AC}{BC} = \frac{3}{4}[/tex]

Hence,

The value of [tex]tan \beta[/tex] in the triangle is [tex]\frac{3}{4}[/tex].

Find out more information about tangent ratio here

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Answer:

5% Dextrose

Step-by-step explanation:

Dextrose is primarily used as a carbohydrate for nutrition and as a source of fluid. Whereas Sodium chloride is primarily used as a source of fluid and electrolytes.

A patient needs fluid and carbohydrates for nutrition. The fluid that the patient is likely to be administered is TNP. The patient needs fluid and carbohydrates for nutrition. The correct option is b.

Total parenteral nutrition (TPN) is a feeding technique that omits the digestive system. The majority of the body's nutritional requirements are met by a specific formula administered intravenously.

When a person cannot or shouldn't receive feedings or fluids orally, the technique is utilized. The term "parenteral nutrition," sometimes known as "total parenteral nutrition," refers to the practice of administering a unique type of food through a vein (intravenously).

The treatment's aim is to treat or stop malnutrition. TPN is made up of many components that are mixed together. These components include dextrose, lipid emulsions, amino acids, vitamins, electrolytes, minerals, and trace elements.

Therefore, the correct option is b, total parenteral nutrition.

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The question is incomplete. Your most probably complete question is given below:

a. protein

b. total parenteral nutrition.

c. iodine

d. fats

Answer:

1) Between 12.5 miles and 21.7 miles.

2) b) 75%

3) c) 95%

4) Between 13.7 miles and 20.5 miles.

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

Chebyshev Theorem:

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]P = 100(1 - \frac{1}{k^{2}})[/tex].

1) According to Chebyshev's theorem, at least 36% of the commute distances lie between miles and miles.

Within k standard deviations of the mean, and k is found when [tex]P = 36[/tex]. So

[tex]P = 100(1 - \frac{1}{k^{2}})[/tex]

[tex]36 = 100 - \frac{100}{k^2}[/tex]

[tex]\frac{100}{k^2} = 64[/tex]

[tex]64k^2 = 100[/tex]

[tex]k^2 = \frac{100}{64}[/tex]

[tex]k = \sqrt{\frac{100}{64}}[/tex]

[tex]k = \frac{10}{8}[/tex]

[tex]k = 1.25[/tex]

Within 1.25 standard deviations of the mean.

1.25*3.7 = 4.6 miles

17.1 - 4.6 = 12.5 miles

17.1 + 4.6 = 21.7 miles

Between 12.5 miles and 21.7 miles.

2) According to Chebyshev's theorem, at least of the commute distances lie between 9.7 miles and 24.5 miles.

17.1 - 9.7 = 24.5 - 17.1 = 7.4 miles, so within 2 standard deviations of the mean, which is 75%, option B.

3) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the commute distances lie between 9.7 miles and 24.5 miles.

Within 2 standard deviations of the mean, by the Empirical Rule, which is 95%, option c.

4) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the commute distances lie between miles and miles.

Within 1 standard deviation of the mean.

17.1 - 3.4 = 13.7

17.1 + 3.4 = 20.5

Between 13.7 miles and 20.5 miles.

Answer:

12

Step-by-step explanation:

so basically

(x^2+2)*(1-3x)=-3x^3+x^2-6x+2

now plug in -1

-3(-1)^3+(-1)^2-6(-1)+2=12

hope this helped :)

The correct value of (fg)(-1) is "12". A further solution of the given query is provided below.

Given functions are:

[tex]f(x) = x^2+2[/tex]

[tex]g(x) = 1-3x[/tex]

Now,

⇒ [tex](fg) = (x^2+2)(1-3x)[/tex]

By applying multiplication, we get

           [tex]=x^2+2-3x^3-6x[/tex]

           [tex]=-3x^3+x^2-6x+2[/tex]...(equation 1)

By substituting the value "-1" in place of "x" in equation 1, we get

⇒ [tex](fg)(-1) = -3(-1)^3+(-1)^2-(6)(-1)+2[/tex]

                  [tex]=-3(-1)+1+6+2[/tex]

                  [tex]=3+1+6+2[/tex]

                  [tex]=12[/tex]

Thus the right answer is (fg)(-1) = 12.

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Answer:

can confirm guy or girl above me

Step-by-step explanation:

The solution to the equation is y=14/15.

The given equation is -3y+2/3=2y-4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, transpose -3y to RHS and simplify.

That is, 2/3=5y-4

Transpose -4 to LHS and simplify.

That is, 14/3=5y

Multiply by 1/5 on both sides of the equation.

So, 14/3×1/5=5y×1/5

⇒y=14/15

Therefore, the solution to the equation is y=14/15.

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Step-by-step explanation:

First car.

0.2 gallons used for 7 miles.

Distance drive on 1 gallon of gas [tex]=\dfrac{7}{0.2}=35\ \text{miles}[/tex]

Second car.

0.5 gallons used for 12 miles.

Distance drive on 1 gallon of gas [tex]=\dfrac{12}{0.5}=24\ \text{miles}[/tex]

Third car.

0.9 gallons used for 25 miles.

Distance drive on 1 gallon of gas [tex]=\dfrac{25}{0.9}=27.8\ \text{miles}[/tex]

So, the first car traveled fast while the second car traveled least. Hence, the sequence is first car > third car > second car.

Perfect square trinomial

[tex] \boxed{ a^2 \pm 2ab+b^2 = (a \pm b)^2 } [/tex]

Using the perfect square trinomial

[tex] p^2 - 4p + 4 = 0 [/tex]

[tex] p^2 - 2(2p) + (2)^2 = 0 [/tex]

[tex] (p-2)^2 = 0 [/tex]

[tex] (p-2) = 0 [/tex]

[tex] p = 2 [/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\bold{p^2-4p+4=0}[/tex]

[tex]\text{FACTOR the LEFT side of your equation}\\\bold{(p-2)(p-2)=0}[/tex]

[tex]\text{SET each of your FACTORS TO EQUAL to 0}\\\bold{p-2=0\ or\ p-2=0}[/tex]

[tex]\text{SIMPLIFY the equations\ above and you will have your answer}[/tex]

[tex]\boxed{\boxed{\bold{Answer: \large\text{\bf{p = 2}}}}}\huge\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

I Think E But Im Not Sure About It

Answer:

4 1/12

Step-by-step explanation:

Answer: 4 1/2

cause it is