O EQUATIONS AND INEQUALITIESSolving a decimal word problem using a linear equation with th.

Answer

KM = 30 units

Tan M = (8/15)

Explanation

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = KM = ?

b = KL = 16

hyp = LM = 34

a² + b² = (hyp)²

KM² + 16² = 34²

KM² + 256 = 1,156

KM² = 1,156 - 256

KM² = 900

Take the square root of both sides

√(KM²) = √(900)

KM = 30 units

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

Using M as the given non-right angle,

Hypotenuse = LM = 34

Opposite = KL = 16

Adjacent = KM = 30

Using trignometric identities, we know that TOA means

Tan M = (Opp/Adj)

Tan M = (16/30)

Divide numerator and denominator by 2

Tan M = (16/30) = (8/15)

Hope this Helps!!!

The rate of increase in water pressure in atm/km = 992 atm/km

Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.

The rate at which Mustafa dives = 0.992atm/meter.

That is,

0.992 atm = 1 meter

X atm = 1 km

But 1000m = 1 km

make X atm the subject of formula;

x atm = 0.992 × 1000

X atm = 992 atm/km

Therefore, the rate in atm/ km would be = 992 atm/km

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Answer:

145 miles

Step-by-step explanation:

870 ÷ 6 = 145

P (A) = probability of a car purchased in 2010's

P (B) = probability of the car being made from ash wood

P (A and B) = 4

P (B) = 4 +3 = 7

Conditional probability:

P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

Answer:

Angle ABD must be congruent to Angle AEC.

Explanation:

Angle: Triangles ADB and ACE share angle A in common.

Side: AD is congruent to AC.

For Triangles ADB and ACE to be congruent by the ASA Congruence Theorem, then the following must hold:

Angle: Angle ABD must be congruent to Angle AEC.

Answer:  [tex]6 \times 10^6[/tex] which is choice B

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

Method 1

5,846,000 rounds to 6,000,000 aka "6 million".

This converts to the scientific notation [tex]6 \times 10^6[/tex]

The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000

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

Method 2

Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.

So we get 5.846

We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again

Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]

Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]

A rhombus have 4 sides and angles

it first must be proven to have 4 sides, or 4 angles

thats a definition for Quadrilateral

then correct option is D

The volume of a cone is given by the formula:

From the question, we are provided with following:

We have to use the given parameters to obtain the radius of the cone.

Thus, we have:

Therefore, the volume of the cone is:

Hence, the correct option is option BH

Equation of parabola in vertex form is 13x² + 26x + 17

Define Parabola

A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.

Given,

vertex (h,k) = (-1, 4)

points (x,y) = (-2, 17)

We know, The equation in vertex form is

y = a(x - h)² + k

put the (h,k) values,

y = a(x - (-1))² + 4

y = a(x + 1)² + 4                     --------- eq(i)

Next, find the value of 'a' by plug in the points of (x, y) in eq(i)

y = a(x + 1)² + 4

⇒17 = a(-2 + 1)² + 4

⇒17 = a(-1)² + 4

⇒17 = a + 4

⇒a = 13

Now, substitute 'a' value in eq(i) to find the equation of parabola

y = a(x + 1)² + 4

⇒ y = 13(x + 1)² + 4

⇒ y = 13(x² + 1 +  2x) + 4

⇒ y = 13x² + 13 + 26x + 4

⇒ y = 13x² + 26x + 17

Therefore, equation of parabola in vertex form is 13x² + 26x + 17

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Answer:

• 17, 20, 25, 29 and 40

• IQR=9

Explanation:

(a)Given the set of values:

{17, 20, 21, 25, 25, 29, 40}​

• The minimum value = 17

The first quartile

The first quartile is the median of the lower half of the data set.

The lower half of the data set = 17, 20, 21

• Therefore, the first quartile =20

The Median

The median is the number in the middle of the set of values.

The number in the middle is 25, therefore:

• Median = 25

The third quartile

The third quartile is the median of the upper half of the data set.

The upper half of the data set = 25, 29, 40

• Therefore, the third quartile =29

Finally, Maximum Value = 40.

The five-number summary of the set of values is: 17, 20, 25, 29 and 40

(b)Interquartile Range

Interquartile Range = Third Quartile - First Quartile

=29 - 20

IQR=9

Question:

Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.​

Solution:

A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:

In this case, the appropriate trigonometric identity is:

where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:

and solving for h, we get:

then, the correct answer is:

The height of the building is 38.85 ft.

Given;

length of the ladder, x = 39 ft

the angle between the ground and the ladder, θ = 85°

let the height of the building be h.

Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.

Apply the following trig ratio to determine the height of the triangle;

sin(θ) = opposite/hypotenuse

sin(85°) = h/39

h = 39sin(85°)

h = 38.85 ft

Therefore, the height of the building is 38.85 ft (approx.).

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ANSWER:

STEP-BY-STEP EXPLANATION:

To calculate the value of the midpoint, we use the formula of the midpoint which is the following:

Replacing and solving the midpoint:

The total track lap time of the runner is 4 11/15 and it has been written as a mixed number or a fraction in lowest terms.

Mixed fraction:

The fraction represented with its quotient and remainder is known as mixed fraction.

Given,

A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk.

Here we need to find the total track lap time of the runner.

Here we can compute the Total Lap Time by multiplying each fraction by its associated lap time, then we get,

   Run Lap Time = (2/5)(3) = 6/5 minutes

   Jog Lap Time = (1/3)(5) = 5/3 minutes

   Walk Lap Time = (4/15)(7) = 28/15 minutes

So, the total lap time is, written as,

   Total Lap Time = 6/5 + 5/3 + 28/15

Now, we have to make the fraction equal to each other,

=> (6x3)/(5x3) + (5x5)/(3x5) + (28 x 1)(15 x1)

=> 18/15 + 25/15 + 28/15  

=> (18 + 25 + 28)/15 = 71/15

Now, we have to convert this into mixed fraction then we get,

=> 71/15 = 4 11/15

Therefore, the total Lap Time is 4 11/15 minutes.

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Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.

The type of inequalities and symbols are:

So, there are four types of inequalities, for example:

Each inequality is different from the other, this means that the symbol used represents a type of inequality.

At last, among the choices, the inequalities are

However, variable inequalities mean that the inequalities must have a variable in it. So, they are:

Therefore, the variable inequalities are b, c, and d.

The total points that the four students score in round 1 is 75 points.

Based on the information given, it's important to convert the numbers to while numbers and then add.

John has 19.5. This will be 20.

Adam had 21.2. This will be 21.

Peter has 23.8. This will be 24.

Grace has 10.2. This will be 10.

The total points will be:

= 20 + 21 + 24 + 10

= 75

The complete question is given below.

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The points of four students are:

John 19.5

Adam 21.2

Peter 23.8

Grace 10.2

About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number

Solution

The answer is

given data:

the amount needed to pay the downpayment of the car = $5280.

original financial plan = $220 per month.

The amount kara saved after 1 year = $2300.

the balance amount she needed to save

now, divide the balance amount by 12, because 1 year =12 months.

Thus, kara needs to save 248 dollors each month in order to have 5280 dollors after a year.

If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

In a certain​ chemical, the ratio of zinc to copper is 4 to 11.

i.e 4:11 or 4 /11

If A jar of the chemical contains 528 grams of copper

We need to find how many grams of zinc does it contain.

Let us consider it as x.

Form a equation,

4/11=x/528

4×528=11x

2112=11x

Divide both sides by 11

192=x

Hence 192 grams of zinc does it contain.

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Given:

Mean,ц = 69.5

Standard deviation, σ = 6.5

Let's solve for the following:

• 3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be?

Apply the z-score formula:

Where:

x = 82

ц = 69.5

σ = 6.5

Thus, we have:

Therefore, the z-score is 1.9

Question 4.

Here, we are to find P(Z<1.9).

Using the standard normal distribution table, we have:

NORMSDIST(1.9) = 0.9712

Now convert to percentage:

0.9712 x 100 = 97.12% = 97%

ANSWER:

3). 1.9

4.) 97%

First, let's sum the single costs of each item.

Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)

Then, we apply a 7% sales tax.

As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.

Data Given:

Nurses = 1 1/2 of each doctor

This can be interpreted as

If there are 6 doctors in the day shift, then there will be

=>

This means that I will have to schedule 9 nurses for the day shift on Friday

1------------------------------------>100%

43/25----------------------------->x%

So, using cross multiplication:

Answer:

Step-by-step explanation:

you can view this,its similar just the numbers are switched.

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Answer:

35

Step-by-step explanation:

sorry if im wrong sorry

1) In this expression, we have already a factored form. So the factor in this expression is 9(y³+9) Because multiplying "distributing it" we'll have the whole expression

6z^4 -4+9(y³+9)

6z^4 -4 +9y³+81

2) 9(y³+9)

(0,1) is a possible coordinite through the points (-3,-3), (3,5)

The domain of the given function is:

Because the domain corresponds to the set of all possible inputs, x-axis.

The range of this function is:

Because the range corresponds to the set of all possible outputs, y-axis.

The given information is