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Solving a word problem on proportions using a unit rate
Ali made $306 for 17 hours of work.
At the same rate, how many hours would he have to work to make $126?

Answer: 59.28

Step-by-step explanation:

your welcome :)

The value of h in the given polygon is 34.8°

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon.

The sum of the interior angles of a regular polygon = (n - 2) x 180

where n = number of sides of the polygon

here n = 20

Sum of the interior angle = (20 - 2) x 180

Sum of the interior angle = 3240°

which also means that 20(5h - 12) = 3240

100h -240 = 3240

100h = 3240+240

100h = 3480

h = 3480/100

h = 34.8°

In conclusion, the value of h = 34.8°

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The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is tan(cos(t)). The derivation will be done as below,

[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]

Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.

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He needs 10 litres of solution of 40% and 20 litres of 70% solution to make 30 litres of 60% acid solution.

According to the question,

We have the following information:

Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution.

Now, let's take x litres of 40% solution and y litres of 70% solution.

So, we have the following expressions:

x+y = 30

x = 30-y ....(1)

40x/100 + 70y/100 = 30*60/100

Dividing 100 on the numerator by 100 on denominator:

40x+70y = 1800

Dividing both sides by 10:

4x+7y = 180

Putting the value of x from equation 1:

4(30-y)+7y = 180

120-4y+7y = 180

120+3y = 180

Subtracting 120 from both the sides:

3y = 180-120

3y = 60

y = 60/3

y = 20

Now, putting this value of y in equation 1:

x = 30-y

x = 30-20

x = 10

Hence, he needs 10 litres of 40% solution and 20 litres of 70% solution to make 30 litres of 60% acid solution.

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Answer:

one ninths

Step-by-step explanation:

1/3-2/9 - fraction calculator. The result is 1/9 ≅ 0.1111111 = one ninth.

The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

Let us solve the given algebraic expression by the long division method:

We are given the expression:

(2x^3 + 3x + 7) / (x^2 + x + 10)

We need to perform the division of the given algebraic expression:

x^2 + x + 10  ) 2x^3 + 3x + 7 ( 2x - 2

                       2x^3 + 2x^2 + 20x

                     -         -            -        

                         -2x^2 - 17x + 7

                         -2x^2 - 2x  - 20

                         +        +       +          

                                  -15x + 27

So,

quotient = 2x - 2

remainder =  -15x + 27

Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

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Answer: -3

Step-by-step explanation:

Answer:

29.16% is spent

you have to divide 350 by 1200 then multiply by 100 then the answer will come

The measures, using the binomial distribution, are given as follows:

a) Probability that exactly six arrive within two days: 0.735 = 73.5%.

b) Probability that exactly five arrive within two days: 0.232 = 23.2%.

c) Mean: 5.7 letters.

d) Variance: 0.285 letters².

e) Standard deviation: 0.534 letters.

The mass function, formula for the probability of x successes, is defined as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the mass function are listed as follows:

Hence, in the context of this problem, the values of these parameters are given as follows:

n = 6, p = 0.95.

The probability that all six arrive within two days is of:

P(X = 6) = 0.95^6 = 0.735 = 73.5%.

The probability that five arrive within two days is:

P(X = 5) = 6 x 0.95^5 x 0.05 = 0.232 = 23.2%.

The statistical measures are calculated as follows:

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Answer:

False

Step-by-step explanation:

x ≤ - 2

the symbol ≤ ( less than or equal to ) means that x can equal - 2 and any values to the left of - 2 on the number line.

- 1 is to the right of - 2 and - 3 is to the left , so

the values represented are - 2, - 3

Answer: Par affluence

Step-by-step explanation: Car chaque 3 min le nombre de client augmentera

The sentence which is true is 5+3×2²=17. The correct option is D.

Given the sentences is 5+3×22=256, 5+3×22=32, 5+3×22=180 and 5+3×2²=17.

We want to choose the sentence which is true.

An operator is a wildcard symbol used to indicate a mathematical operation that results in one or more mathematical objects leading to another similar object.

The first option is 5+3×22=256.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The first option 5+3×22≠256.

The second option is 5+3×22=32.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The second option 5+3×22≠32.

The third option is 5+3×22=180.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The third option 5+3×22≠180.

The fourth option is 5+3×2²=17.

Solve the LHS, we get

5+3×2²=5+3×4

5+3×2²=5+12

5+3×2²=17.

The fourth option 5+3×2²=17.

Hence, the sentence which is true from the given sentences is 5+3×2²=17.

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in this situation Zero represents, The surface of the water

-4 represents the sand that lies under 4 feet of water.

4 represents a branch 4 feet above the water.

Upon analysis, it can be said that as we move downwards, the value increases in negative sign

As we move upwards, the value increases in positive sign

The surface of water becomes the origin, as it is zero.

Therefore, , in this situation Zero represents, The surface of the water

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Answer:

1-3+2-5+-1-11

Step-by-step explanation:

I hope this helps :’)

From the number line √90-√40 match with D, [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C, 2√27 -√48 match with E and [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.

In the given question we have to match the each expession with its position on the number line.

The given first expression is √90-√40.

We firstly simplifying the expression.

√90-√40=√9×10-√4×10

√90-√40=3√10-2√10

Taking common [tex]\sqrt{10}[/tex] on both side

√90-√40=√10(3-2)

√90-√40=√10

√90-√40=3.16

From the number line √90-√40 match with D.

The given second expression is [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex].

We firstly simplifying the expression.

We can write it as

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{5\times7}-\sqrt{6\times7}}{\sqrt{5}-\sqrt{6}}[/tex]

Taking common √7 on both side

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{7}(\sqrt{5}-\sqrt{6})}{\sqrt{5}-\sqrt{6}}[/tex]

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\sqrt{7}[/tex]

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] = 2.65

From the number line [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C.

The given third expression is 2√27 -√48.

We firstly simplifying the expression.

We can write it as

2√27 -√48=2√3×9 -√16×3

2√27 -√48=2×3√3 -4√3

2√27 -√48=6√3 -4√3

Taking √3 common on both side, we get

2√27 -√48=√3(6 -4)

2√27 -√48=2√3

2√27 -√48=2×1.71

2√27 -√48=3.42

From the number line 2√27 -√48 match with E.

The given fourth expression is [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex].

We firstly simplifying the expression.

We can write it as

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{9\times6}-\sqrt{4\times6}}{\sqrt{2\times9}-\sqrt{2\times4}}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{3\sqrt{6}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{2}}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{6}(3-2)}{\sqrt{2}(3-2)}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\sqrt\frac{6}{2}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] =√3

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] = 1.71

From the number line [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.

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Answer: d,c,e,

ur welcomee!

The missing statement and the reason of LN bisects ∠MLO, LM≅LO are given and ∠OLN≅∠MLO is because of definition of angle bisector, LN≅LN is because it is common to both the angles ∠LNO AND ∠LNM, LO≅LM is because ΔLNO and ΔLNM both are congruent.

Given that:

LN bisects ∠MLO and LM≅LO

Prove that: ΔLMN ≅ ΔLON

In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.

Hence, using this we will prove that the triangles are congruent by ASA congruence rule.

In ΔLON and ΔLMN

Side ON ≅ Side MN

∠LNO ≅ ∠LNM ( ∵ common angle)

∠ONL ≅ ∠MNL (∵ Given as LN is the angle bisector of ∠MLO)

⇒ ΔLMN ≅ ΔLON ( By ASA congruence theorem).

Statement 1: LN bisects ∠MLO

Reason: Given.

Statement 2:  LM≅LO

Reason: Given.

Statement 3: ∠OLN≅∠MLO

Reason: Definition of angle bisector.

Definition of angle bisector: An angle bisector is defined as a line segment that bisects one of the vertex angles of a triangle.

Statement 4: LN≅LN

Reason: Common to both the angles ∠LNO AND ∠LNM and also these angles are 90° because angle made by angle bisector is always 90°.

Statement 5: LO≅LM

Reason: ΔLNO and ΔLNM both are congruent.

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Answer:

C

Step-by-step explanation:

1000*0.04 = 40

(9/12) * 40 = 30

Answer:

y intercept: 1

X intercept: 4

Step-by-step explanation:

to find y intercept we set x to 0

0+4y=4

   /4.  /4

  y=1

y intercept is 1

Now for x intercept we set y to 0

x+4(0)=4

x=4

X intercept is 4

Hopes this helps please mark brainliest

To answer this question we will use The Linear Programming concept

The formula for the moose population is

The moose population in 2006 would be

We use the year 1990 as the base year for creating the equation of the moose population. We could assume that:

The moose population of the year: P(x)

The moose population in year 1990: a

The year difference to 1990: x

The linear change of the moose population: b

Hence, we could make some assumption about the relationship between each elements mentioned above, where the moose population of the year would be depends on the linear change of the population added into the original moose population in year 1990. We could write this relationship into the equation (i):

P(x) = a + bx ... (i)

Using data provided from the question, we could make some other equations and find the value of b:

P(x) = a + bx

P(4) = a + 4b = 3280 ---> year 1994 ... (ii)

P(7) = a + 7b = 4120 ---> year 1997 ... (iii)

We could do some eliminations between equations (ii) and (iii)

3280 = a + 4b

4120 = a + 7b -

840 = 3b

b = 280 ... (iv)

After finding the value of b, we could subtitute its value into equation (ii) to find the value of a:

3280 = a + 4b

3280 = a + 4(280)

3280 = a + 1120

a = 2160 ... (v)

After finding the value of a and b, we could rewrite the equation (i) by inserting the and b values.

P(x) = a + bx

P(x) = 2160 + 280x ... (vi)

Next, we will predict the moose population to be in 2006.

First, we should determine the value of x, the difference between the year 2006 to the base year 1990.

x = 2006 - 1990

x = 16 ... (vii)

We would subtitute the equation (vii) into equation (vi) to predict the moose population to be in 2006:

P(16) = 2160 + 280(16)

P(16) = 6640...(viii)

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Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex] \sf8 : 2 :: x : 6[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\boxed{\: x = \frac{8 \times6}{2} = \frac{48}{2} = 24 }[/tex]

Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{8 : 24 :: 6}[/tex]

Answer:

x = 130

Step-by-step explanation:

x - 37 = 93 ( add 37 to both sides )

x = 130

Answer:

x=130

Step-by-step explanation:

x-37=93

x=93+37

x=130

x-37=93

-37-93= x (- / - =+ )

130=x

So, your answer is 130

The height of the triangle pictured in the question is 2 units.

According to the question,

We have the following information:

Area of triangle = 8

Base of triangle = 8

We know that the following formula is used to find the area of triangle:

Area of triangle = 1/2*base*height

Area of triangle = 1/2*8*height

8 = 4*height

Dividing by 4 on both the sides:

Height = 8/4

Height of the triangle = 2 units

(Note that every physical quantity has some units of measurements. For example, the unit of measurement of area is square units.)

Hence, the height of the triangle pictured in the question is 2 units.

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Answer:

Step-by-step explanation:

(4096)ˣ  = 8

log ₂ (4096)ˣ = log ₂ 8

x·log ₂ (4096) = log ₂ 8

x = log ₂ 8 / log ₂ (4096)

x = log ₂ 2³ / log ₂ 2¹²

x = 3 / 12

x = 1 / 4

The value of the linear correlation coefficient r is of:

m = -1.

A linear equation is a special function that has the format of the equation given as follows:

y = mx + b.

The coefficients of the equation y = mx + b are given as follows:

In this problem, the points of the function are listed as follows:

(1 , 6) , (3 , 4) and (5 , 2)

From these three points, we can gather that when x increases by 2, y decays by 2, hence the slope of the linear function is given as follows:

m = -2/2 = -1.

Meaning that the linear correlation coefficient r of the linear function is of r = -1.

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Answer:

the sum of squares kasi yan

Explanation:

first find the squareroot of a² and 100

the squareroot of a²=a

because a×a=a²

the squareroot of 100=10

because 10×10=100

second factor

(a + 10)² or (a + 10)(a + 10)

In this backgammon game, the probability used is Classical one.

Probability:

Probability refer the possible way of happening the particular event.

Given,

Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.

Here we need to identify whether the given probability is empirical or classical.

In order to find the type of probability, first we have to know the definition of each of them.

So, classical probability means the the statistical concept that measures the likelihood (probability) of something happening where as the empirical probability means the  probability that is based on historical data.

Therefore, based on the definition, the given situation is purely based on the classical probability.

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a) At t = 0days : 300insects

b) The growth rate is 5.12% each day.

c) Population after 10days: P(10) =494.61

d) The population to reach 420 is equals roughly 70.129 hours

e) The insect population double in  t=6.020 days , which is 144.48 hours.

What is Population?

Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.

Given: t in days, P(t)=300e(0.05t).

(a) The total number of insects at time t=0 days is equal to

P(0)=300(1)

P(0) =300.

(b) The growth rate is calculated as the percentage increase over time, which is equal to-

P(t+1)/P(t)=300e(0.05(t+1))/300e(0.05t)

P(t+1)/P(t) =e^(0.05(1))

P(t+1)/P(t) =1.0512

Therefore, the growth rate is 5.12% each day.

(c) Population after 10 days.

P(10)=300e^(0.05*10)

P(10) =300(1.6487)

P(10) =494.61

(d) When P(t)=420, the population will reach 420,

or 300e0.05t=420,

take log

0.05t=log(1.4), or

t = 2.922 days,

for the population to reach 420.

equals roughly 70.129 hours

(e) When P(t)=2*300=600 the population will double.

300e^(0.05t)=600

=> e^(0.05t)=600/300=2

Take log

(log 0.05t=log(2)),

t=6.020 days , which is 144.48 hours.

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The solved answer for the given fraction expression in will be 2.6833.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Given X = 1/3

Y = 3/5

Z = 2 1/4 = 9/4

The value of X*Y*Z = (1/3*3/5*9/4)

= (20+36+105)/60

=161/60

=2.6833

Hence the solved answer for the given expression will be 2.6833.

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Answer:

It is a binomial, so it is (ax+b)^2. In this case, a=3, b=-8, and there are 2 terms. The constant is 64 and the leading coefficient is 9.