The measures of the angles of a triangle are shown in the figure below. Solve for x.

We can take square root of the expression given on the right hand side of equation (1) anytime,

hence there are no any interval restrictions. The largest interval is (-∞, ∞).

Given initial value problem is;

dy/dx = √y, y(xo) = yo

Solve for y(x)

Integrate both sides of the differential equation with respect to

x∫ dy/√y = ∫ dx0.5 ∫ 1/√y dy = x + c,

where c is constant of integration

0.5[2√y] = x + c√y = (x + c)^2y = (x + c)^4 ......(1)

Using the initial condition y(xo) = yo yo = (xo + c)^4c = y^(1/4) - xo

Substitute the value of c into equation

(1)y = (x + y^(1/4) - xo)^4

Find the largest interval I on which the solution is defined

Since y0 > 0y = (x + y^(1/4) - xo)^4 > 0

Take fourth root of both sides y^(1/4) > 0

That means that we can take square root of the expression given on the right hand side of equation (1) anytime,

hence there are no any interval restrictions.

The largest interval is (-∞, ∞).

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Answer:

$695.94

Step-by-step explanation:

25% of 856 = 214

6.3% of 856 = 53.928

856 + 53.928 = 909.928

909.928 - 214 = 695.928 about 695.94

Answer:

695.93

Step-by-step explanation:

75% of 856 is 642

642 + 53.93 = 695.93

6.3 = 53.93

Answer:

d

Step-by-step explanation:

there are six triangles and two rectangles

Answer:

D. For every 6 triangles there are 2 rectangles.

Answer:

142

Step-by-step explanation:

50:284*100 =

(50*100):284 =

5000:284 = 142

Definition = the word OF means to multiply

Hope this helps!

                                                                                                  -  Tobie the dog

Answer:

Fantasia's family's car is more fuel-efficient.

Step-by-step explanation:

Given that, Tiyleah's family's car is getting 40 miles per gallon, and Fantasia's family's car uses 7 liters per 150 km.

The comparison can be done by observing the distance traveled by the cars in an equal amount of fuel. The car which covers more distance in an equal amount of fuel is more fuel-efficient.

First, convert the given units to have the same unit of measurement,

As 1 gallon =3.7854 liters and 1 mile = 1.609344 km

So, 40 miles =40 x 1.61=64.40 km

Now, The distance covered by Tiyleah's family's car is 64.40 km in 3.7854 liters.

So, the distance covered by Tiyleah's family's car in 1 liter of fuel is \(\frac{64.40}{3.7854}=17.01\) km

In a similar way,

As Fantasia's family's car uses 7 liters per 150 km.

So, the distance traveled by Fantasia's family's car in 1 liter of fuel =150/7=21.43 km

Observe that, in 1 liter of fuel, Tyleah's family's car covered 17.01 km while Fantasia's family's car covered 21.43 km which is more.

Hence, Fantasia's family's car is more fuel-efficient.

Answer:

= 8 mp /h

Step-by-step explanation:

Average speed=total distance/total time

=20/2.5

=8 mp/h

Answer:8mp/h

Step-by-step explanation:

Answer:

Drawing the first marble would be 4/17 then putting that one aside and picking another green marble would be 3/17

Step-by-step explanation:

a) To construct the appropriate quality control chart, we will use the p-chart, which is used for proportion data.

First, we need to calculate the overall proportion of unsatisfactory meals in the January survey:

Proportion of unsatisfactory meals = (74 + 42 + 64 + 80 + 40 + 50 + 65 + 70 + 40 + 75) / (1000 x 10) = 0.0665

Next, we calculate the center line and control limits of the p-chart:

Center line = p-bar = 0.0665

Upper control limit (UCL) = p-bar + 3sqrt((p-bar(1-p-bar))/n) = 0.109

Lower control limit (LCL) = p-bar - 3sqrt((p-bar(1-p-bar))/n) = 0.024

b) In April, another 3-day survey was conducted, and the numbers of unsatisfactory meals were 100, 80, 130, respectively.

We need to calculate the proportion of unsatisfactory meals for the April survey:

Proportion of unsatisfactory meals = (100 + 80 + 130) / (3 x 1000) = 0.1033

Next, we check if the process is in control in April by comparing the proportion of unsatisfactory meals to the control limits calculated from the January survey.

LCL = 0.024

UCL = 0.109

Since the proportion of unsatisfactory meals in April (0.1033) is within the control limits (0.024 to 0.109), we can conclude that the process of serving lunch is still in control in April. However, the proportion of unsatisfactory meals has increased from January to April, which may warrant further investigation and improvement efforts.

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-1.08333333333

I used a calculator

hope it helps!

Answer:

\(-1.083\)

Step-by-step explanation:

If you want to convert \(\frac{-26}{24}\) as a fraction, you will have to divide the numerator by the denominator.

\(-1.083\)

\(Aaishathameem\)

Answer:

5 units were bought

Step-by-step explanation:

Firstly, let us calculate the total amount paid

If what was paid was $9.45, this cost includes the price of the coupon subtracted

Returning the coupon price, we have the total as;

9.45 + 0.5 = $9.95

So to get the number bought, we divide this total by the price for one

We have this as;

9.95/1.99 = 5

Answer:

5 units

Step-by-step explanation:

9.95/1.99 = 5

Answer:

D

Step-by-step explanation:

I tried the last one and it did not work so maybe D

It will take approximately 12 years for a deposit of $1,085.00 to grow to $1,813.00 with an interest rate of 11.00%.

To determine the number of years required for the deposit to grow, we can use the formula for compound interest : A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that P = $1,085.00, A = $1,813.00, r = 11.00%, and the interest is compounded annually (n = 1), we can rearrange the formula to solve for t. The equation becomes:

$1,813.00 = $1,085.00(1 + 0.11)^t

Dividing both sides by $1,085.00:

1.67 = (1.11)^t

Taking the logarithm of both sides:

log(1.67) = t * log(1.11)

Solving for t:

t = log(1.67) / log(1.11)

Using a calculator, we find that t is approximately 12 years. Therefore, it will take approximately 12 years for the deposit to grow from $1,085.00 to $1,813.00 with an interest rate of 11.00%.

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Answer:

14(ab- 3a)

Step-by-step explanation:

14 times ab is 14ab and 14 times 3a is 42a

A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours

Given,

Chance Product is designed to function for 10,000 hours

of failure is 3%

To find,

Average number of failures per hour

MTTF

Solution,

Average number of failures per hour = Chance of failure/Total hours of function

= 3%/10000

= 0.03/10000

= 0.000003

MTTF = 1/Average number of failures per hour

= 1/0.000003

= 333,333 hours

The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.

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RNA's capability to self-replicate and catalyze chemical reactions make it the best candidate for the first life-form.

According to the scientists, RNA is considered the best candidate for the first life-form due to the fact that RNA is capable of self-replication and catalysis. This is possible because RNA can act both as a template to produce copies of itself and also as an enzyme to accelerate chemical reactions. These abilities suggest that RNA could have played a role in the emergence of the first living organisms on Earth.

An RNA molecule has the ability to catalyze reactions, which means that it can speed up chemical reactions without itself being altered. Thus, it is capable of serving as an enzyme. Scientists believe that the first life-form must have been capable of self-replication and catalysis, and RNA is capable of both functions.

This capability is significant because it is fundamental for the origin of life. Hence, RNA is believed to have played a significant role in the emergence of the first living organisms on Earth.

To conclude, RNA's capability to self-replicate and catalyze chemical reactions make it the best candidate for the first life-form.

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RNA is considered the best candidate for the first life-form by scientists because RNA is capable of self-replication and catalysis.

The correct option is the first one due to following reasons:

As a result, scientists believe that RNA may have played a crucial role in the origins of life on Earth.

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Answer:

57

Step-by-step explanation:

100 - 43 =

57

Answer:

He got 57% wrong

Step-by-step explanation:

If he got 43% correct, there is 100 percent on the assignment

100 -43 = 57

He got 57% wrong

Answer:

A) 11,752.8 feet

B) 105,715.8 feet

C)The helicopter

Step-by-step explanation:

Helicopter:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(5280^{2}\) + \(10500^{2}\) = \(c^{2}\)

27878400 + 110250000 = \(c^{2}\)

138128400 = \(c^{2}\)

\(\sqrt{138128400}\) = \(\sqrt{c^{2} }\)

11752.8 ≈ c  Answer is rounded to the nearest tenth

Plane:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(4500^{2}\) + \(10560^{2}\) = \(c^{2}\)

20250000 + 11155584400 = \(c^{2}\)

11175834400 = \(c^{2}\)

\(\sqrt{11175834400}\) = \(\sqrt{c^{2} }\)

105715.8 =c Rounded to the nearest tenth

Answer:

Step-by-step explanation:

Use ratios to solve it:

x =  1*21 3/4 ÷ 6 1/2 =

      21 3/4 ÷ 6 1/2 =

      87/4 ÷ 13/2 =

      87/4 × 2/13 =

      87/26 =

      3 9/26

The equation 2y  = 10x - 16 in standard form is  10x - 2y = 16 where A = 10, B = - 2 and C = 16

Linear equation can be represented in various form such as general form, standard form, slope intercept form and point slope form.

Therefore, linear equation in standard form can be represented as follows:

Ax + By = C

where

Therefore, let's write 2y  = 10x - 16 in standard  form.

2y  = 10x - 16

Hence,

10x - 2y = 16

Therefore,

A = 10

B = - 2

C = 16

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Answer:

She is 12 feet abouv ground.

Step-by-step explanation:

Answer:

Eleven thousand five hundred and twenty

Step-by-step explanation:

E2021

Answer:

Explanation:

Given 4x + 6y - 10x + 13y = 11

If (1, 1) is a solution, then substituting x = 1 and y = 1 into the left hand side of the equation gives 11.

Doing this, we have:

4(1) + 6(1) - 10(1) + 13(1)

= 4 + 6 - 10 + 13

= 13

Answer:

(0,4)

Step-by-step explanation:

Here, we want to find the y-intercept of the quadratic function

g(x) = 5x^2 + 9x + 4

Mathematically, we know that the y-intercept is the position on the graph where we have x = 0

so, to find the y-intercept value, we have to find g(0)

simply put, we have to substitute the value of 0 for x

Mathematically, we have this as;

g(0) = 5(0)^2 + 9(0) + 4

g(0) = 0 + 0 + 4

g(0) = 4

thus, we have the y-intercept point as (0,4)

Answer:

QT = 18

Step-by-step explanation:

Answer:

because of them is bigger than the other one so that means its differ but it has the same length

Step-by-step explanation:

Answer:

\(\sqrt{2}\) and 4\(\sqrt{11}\)

Step-by-step explanation:

To simplify like surds, add/ subtract the coefficients.

(a)

\(\sqrt{2}\) (6 - 5)

= \(\sqrt{2}\) (1)

= \(\sqrt{2}\)

(b)

\(\sqrt{11}\) ( 1 + 3)

= \(\sqrt{11}\) (4)

= 4\(\sqrt{11}\)

Answer:

costo 62 y paseos 13

Step-by-step explanation:

porque si