Solve the right triangle if the hypotenuse is 5 and one acute angle is 34°. Round answers to two decimal places.

The World Health Organization (WHO) sets standards for Oral Rehydration Salts (ORS) which are used to treat dehydration, particularly in children.

The old formula for ORS packets recommended by the WHO contained 75 mM (millimoles) of sodium chloride, which is equivalent to 3.5 grams of salt per liter of water. The new formula for ORS packets recommended by the WHO contains 65 mM (millimoles) of sodium chloride, which is equivalent to 3.0 grams of salt per liter of water.

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Answer:

To find the mean (average) of a set of numbers, we add them together and divide by the number of items in the set.

The first step is to convert all the fractions into a common denominator. In this case, the least common multiple of 3, 3, and 4 is 12.

2 1/3 = 7/3

3 2/3 = 11/3

5 1/4 = 21/4

Now we can add these numbers together:

7/3 + 11/3 + 21/4 = (7 + 11 + 21) / 3 = 39/3 = 13

There are three numbers, so we divide by 3.

Mean = 13/3 = 4 1/3

So the mean of 2 1/3, 3 2/3 and 5 1/4 is 4 1/3.

Step-by-step explanation:

First you turn the equation into y=mx+b form.

2y-3x=10

2y=3x+10

2y/2=(3x+10)/2

y=3/2x+5

Next you take the opposite of the slope.

Slope = 3/2

Opposite = 2/3

Then you insert your values into y-y1=m(x-x1)

y+1=2/3(x+8)

y+1=2/3x+16/3

The answer is

y=2/3x+13/3

Answer:

[tex]56.7[/tex] degrees

Step-by-step explanation:

The distance of [tex]115[/tex] degrees from [tex]98.6[/tex] degrees is [tex]115 - 98.6 = 16.4[/tex] while the space of [tex]56.7[/tex] degrees from [tex]98.6[/tex] degrees is [tex]98.6-56.7 = 41.9[/tex], so the answer is [tex]56.7[/tex].

Answer:

1. HK = 24

2. x = 13

3. x = -26

4. ∠ABC = 120°

Step-by-step explanation:

(1) In all parallelograms, the diagonals bisect each other, or split each other into two congruent (same) halves.

We are given parallelogram HJKL. Its diagonals are HK and JL, because they both are segments that connect two opposite vertexes.

This means that HK and JL are bisected.

Thus, HM is half of HK.

Let's make an equation to represent this situation and solve for HK.

[tex]HM = \frac{1}{2}HK[/tex]

⇒ [tex]12 = \frac{1}{2}HK[/tex] . . . . . . substitute known values

⇒ [tex]12(2) = \frac{1}{2}HK(2)[/tex] . . . . . . multiply the LHS and RHS by 2 to isolate HK

⇒ ∴ [tex]24 = HK[/tex] . . . . . . compute

(2) This problem is similar to #1, so we can use the same concepts as #1.

However, we are given an expression instead of integers.

The only thing that's different about this problem is that we need to solve for x, not a diagonal or part of a diagonal.

VX and UW are the diagonals of parallelogram UVWX.

Thus, VX and UW are bisected.

Thus, the VY and YX are the same length, because they are split in half.

Let's make an equation to represent this situation and solve for x.

[tex]VY = YX[/tex]

⇒ [tex]80 = 6x + 2[/tex] . . . . . . substitute the known values

⇒ [tex]78 = 6x[/tex] . . . . . . . . . subtract 2 from the LHS and RHS

⇒ ∴[tex]13 = x[/tex] . . . . . . . . . divide both sides by 6 to isolate x

(3) This problem uses the exact same concepts and steps as #2.

Thus, RS and SP are the same length.

Let's make an equation to represent this situation and solve for x.

[tex]RS = SP[/tex]

⇒ [tex]65 = -2x - 7[/tex] . . . . . . . . substitute the known values

⇒ [tex]72 = -2x[/tex] . . . . . . . . . . . add 7 to the LHS and RHS

⇒ ∴[tex]-36 = x[/tex] . . . . . . . . . . . divide both sides by -2 to isolate x

(4) In a parallelogram, the opposite angles are congruent (the same).

In parallelogram ABCD, we are given ∠CDA and asked to solve for ∠ABC.

∠ABC and ∠CDA are opposite angles.

∠CDA = 120°

∠ABC = ∠CDA

∴ ∠ABC = 120°

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The parallelogram HJKL is handed to us. The segments HK and JL, which both link two vertexes that are in opposition to one another, serve as its diagonals, triangle HK = 24;  x = 13;  x = -26; ∠ABC = 120°

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

All parallelograms have diagonals that cut them in half or divide them into two congruent (same) halves.

HK = 24, x = 13, x = -26, and ABC = 120 degrees.

The parallelogram HJKL is handed to us. The segments HK and JL, which both link two vertexes that are in opposition to one another, serve as its diagonals.

As a result, HK and JL are divided. HM therefore makes up half of HK.

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Answer:

yup! its true. They are supplementary angles.

Step-by-step explanation:

The number of points scored by Howie and Theo is 600 (Nearest Hundred)

Addition in mathematics is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

from the table,

Howie scored 272 points

Theo scored 325 points

By adding their scores

=272 + 325

=597

Rounding off to the nearest Hundred, 597=600

Hence, Howie and Theo scored 600points

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After rewriting the given equation, we have the resultant equations as (B) -2.3p - 10.1 = 6.49p - 4 and (C) -230p - 1010 = 650p - 400 - p.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

So, we have the equation:
2.3p - 10.1 = 6.5p - 4 - 0.01p

Now, we can rewrite them as follows:

-2.3p - 10.1 = 6.49p - 4

-230p - 1010 = 650p - 400 - p

Therefore, after rewriting the given equation, we have the resultant equations as (B) -2.3p - 10.1 = 6.49p - 4 and (C) -230p - 1010 = 650p - 400 - p.

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Correct question:

Use properties to rewrite the given equation. ch equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

a. 2.3p - 10.1 = 6.4p - 4

b. 2.3p - 10.1 = 6.49p - 4

c. 230p - 1010 = 650p - 400 - p

d. 23p - 101 = 65p - 40 - p

e. 2.3p - 14.1 = 6.4p - 4

Answer:

Step-by-step explanation:

y×8=8y

8y+4=4×7

8y+4=28

8y=24

y=

Answer:

The number is:

3

Step-by-step explanation:

8a + 4 = 4*7

8a + 4 = 28

8a = 28 - 4

8a = 24

a = 24/8

a = 3

Check:

8*3 + 4 = 4*7

24 + 4 = 28

The value of the expression (x - 5y) at y = 5 and x = 47 will be 22.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x - 5y)

The value of the expression at y = 5 and x = 47 will be given as,

⇒ 47 - 5 (5)

⇒ 47 - 25

⇒ 22

The value of the expression (x - 5y) at y = 5 and x = 47 will be 22.

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The complete question is given below.

y = 5 and x = 47. Find the value of the expression (x - 5y).

Jack worked 40 hours a week with fractions of something because he had been employed at the time.

To represent a whole, any number of equal parts or fractions can be utilized. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyze something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolize half of a whole number or object.

given

40-hour work week

jack worked 40  hours in a week

Jack worked 40 hours a week with fractions of something because he had been employed at the time.

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Answer:

Step-by-step explanation:

yooooooooooooooooooo

Answer:

1. Growth

2. Decay

3. Decay

Step-by-step explanation:

Growth means as x increases, y increases too. On the other hand, decay means as x increases, y decreases. There's the theory for exponential function regarding this growth and decay.

Growth

If the base is not a decimal or a fraction then it's growth.

Decay

If the base is a decimal or a fraction then it's decay.

From the problem, first function has base of 5. Hence, it's growth. On the other hand, second and third function both have decimal and fraction as the base. Hence, it's decay.

When considering growth or decay graph, we can ignore the coefficient since it doesn't determine the growth and decay. The only thing that determines if a function increases or decreases is the base under the exponent.

===========================================

Work Shown:

A = final value = 38750

P = amount loaned = 25000

i = interest

i = A - P = 38750 - 25000 = 13750

Now apply the simple interest formula to solve for t.

i = P*r*t

13750 = 25000*0.055*t

13750 = 1375*t

t = 13750/1375

t = 10 years to pay off the loan

Side note: r = 0.055 is the decimal form of 5.5%

The required solution of the simultaneous equation is given as x = 10 and y = -1.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given equations,
x – y = 11  - - - - - (1)
2x + y = 19 - - - -- -(2)

Put x form equation 1 in equation 2
2 [11 + y] + y = 19
y = -1

Now,
x = 11 + y
x = 10

Thus, the required solution of the simultaneous equation is given as x = 10 and y = -1.

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Answer:

i think it will be 16% percent increase in the value of the painting

Answer:

60% increase

Step-by-step explanation:

The painting increases from 120 000 to 192 000 <==== a 72 000 increase

72 000 is what percent of 120 000 ?

   72 000 / 120 000    x  100% =  60% increase

Answer:

5/54

Step-by-step explanation:

Substitute 8 for X, then solve

-5 / 8 (-8) + 10

-5 / -64 + 10

-5 / -54

5/54

Answer:

The cost of renting a car can be represented by the expression:

C = 30m + 0.25m

Where C is the total cost, 30 is the fixed cost per day, and 0.25 is the cost per mile.

Step-by-step explanation:

The linear equation L, which is a translation of line M, can be written as:

y = (2/3)*x - 2

So the correct option is the last one.

First, we need to find the equation of line M.

Remember that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = -2, then we wll get:

y = a*x - 2

And we can also see that the line passes through (-3, -4)

Replacing these values we will get:

-4 = a*-3 - 2

-4 + 2 = -3a

-2/-3 = a

2/3 = a

So line M is:

y = (2/3)*x - 2

And line M is a translation of 3 units down and 2 units left of L, then L is a translation of 3 units up and 2 units to the right, then we can write line L as:

y = (2/3)*(x - 2) - 2 + 3

y = (2/3)*x + (2/3)*-2 - 2 + 3

y = (2/3)*x - 4/3 + 1

y = (2/3)*x - 1/3

So the correct option is the last one.

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Option D is the correct answer. The probability that a test correctly rejects a false null hypothesis is called the significance level.

The significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant.

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta). The quantity (1 - β) is called power, the significance level is the probability of rejecting the null hypothesis when it is true.

For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

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Answer: When dividing two fractions you simply multiply the first one by the reciprocal of the second:

1

4

3

5

=

1

4

⋅

5

3

=

5

12

Answer:

Step-by-step explanation:

(8 + 24) ÷ (12 x 4) = 2/3

Answer: 1440

Step-by-step explanation:

A degree 6 polynomial results from multiplying a degree 2 polynomial by a degree 4 polynomial.

In algebra, a symbol (typically a letter) denotes an unknown numerical value in a formula or algebraic expression. A quantity that can be changed and is not fixed is known as a variable. Numeric and category variables are the two main types. Subcategories are then established for each category for categorical and numerical variables, respectively, using nominal or ordinal and discrete or continuous categories. A brief summary of various types is provided in this section. a metric that is open to a wide range of interpretations. a component of a scientific experiment that may be subject to change; the sign of a variable; something that is variable.

given

The first step is to multiply the first term inside the first parenthesis by each term inside the second parentheses.

The second term in the first parenthesis is now multiplied by every phrase in the second parentheses, and the results are then added to the first terms.

A degree 6 polynomial results from multiplying a degree 2 polynomial by a degree 4 polynomial.

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Answer:

8

Step-by-step explanation:

First look at the left, under the weight 2 there are 2 little boxes one of them is 1. so the other one must be one.  that'll make this small group 2+1+1 =4, which means the other side to balance it, it is also 4.

now we've got 2*4 = 8 under 13. so left side total = 13+8 = 21

now look at the right side, it also must be 21. we already know there is a 5, then under neath the 5, to balance the remaining weight 21-5 = 16, each side must be equal. so each side = 8.  

watermelon itself is one side, so it's 8.

Answer:The most efficient step to finding the solution to the given inequality is, to subtract 4 from both sides. Option D is correct.

Given that,

To determine which step is the most efficient way to find the solution of x + 4 > -8.

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm. Functions are typically denoted by the letter f. (x). The input contains an x.

Here,

=> f(x) = 3x³ + 2

=> g(x) = 3√ x-2 / 3

For ,

=> f(g(x)) =   3x³ + 2

=>  f(g(x)) = 3(3√ x-2 / 3)³ + 2

=>   f(g(x)) = (9/√x - 2/3)³ + 2

Thus ,

Option 2 is correct.

Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

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Since RQ is congruent to PS and RS is congruent to QP, QT = SU, therefore QT and SU are congruent which means PT and RU are also congruent

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

One the property of a parallelogram is that the opposite lines are parallel and congruent.

Therefore RQ = PS ( they are both congruent)

PS = RS ( they are both congruent )

Therefore the measure of line PT = line SU = QT.

This means that the value of PT = R U , we can therefore say that PT and RU are congruent.

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In testing for the equality of k population means that the number of treatments is K. option(b) is the correct answer.

The average treatment deviation is significantly correlated with the average error deviation when the k population means are truly unique from one another. N is the total number of observations included in the analysis, and k is the number of independent groups, in this case, k=4. Hence, option B is the relevant choice.

The two-sample t-test, also known as the independent samples t-test, is a method for determining whether or not the unknown population means of two groups are equal. When your data values are independent, randomly picked from two normal populations, and the variances of the two independent groups are equal, you can utilise the test.

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A constant speed to complete ride is 4 minutes

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