2h + 7 = 3 what does h equal

Answer:

f (t) ≈ 12,119(0.93)t, where t represents the number of years after 1990

Step-by-step explanation:

The exponential function will be \(f(t) = 12119(0.93)^t\). The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

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.

Exponents are used in exponential equations, as the name suggests. We are aware that a number's exponent (or base) tells us how many times the original number has been multiplied.

In the table, the data of the building is given for 1990 the cost is 12,100 and for 1992 the cost is 10,498.

The exponential expression is written as:-

\(f(t) = 12119(0.93)^t\)

For 1992 the time will be t = 2 years

\(f(t) = 12119(0.93)^2\\f(t) = 10490\)

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Answer:

-98=-7h

h

step-1:define

-98=-7h

step-2: rewrite

-7h=-98

step-3:divide both sides by -7

-7h/-7=-98/-7

ANS:

h=14

Answer:

h=14

I hope it is the correct answer

Answer:

The slope-intercept form of line that passes through the point (-2,8) and has a slope of 5/2 is

\(y=\frac{5}{2}x + 13\)

Step-by-step explanation:

Equation of line in point-slope form is

\(y-y_1=m(x-x_1)\) ---------- (1)

Here

\(m=\frac{5}{2} \ \ \ and \ \ \ (x_1, y_1) = (-2, 8)\)

Substituting values in equation (1)

\(y-8=\frac{5}{2} (x + 2)\)

Simplifying it further

\(y=\frac{5}{2}x + \frac{5}{2}2 +8\)

\(y=\frac{5}{2}x + 5 +8\)

\(y=\frac{5}{2}x + 13\)

This is equation in slope-intercept form

Converting 51 liters to gallons, we get 13.47 gallons. So, you could fill up 13.5-gallon containers.

One gallon is equal to 3.78541 liters. To convert liters to gallons, we can divide the number of liters by 3.78541. In this case, we have a maximum capacity of 51 liters, which is equivalent to 51/3.78541 = 13.47 gallons.

Since we cannot fill a partial gallon, we round the answer to one decimal point and get 13.5 gallons.

Therefore, we could fill up 13.5-gallon containers with the maximum capacity of the barrel.

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The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

let,

√x-5=ky

x=30 when y=2

√30-5=2k

or, k=(√30-5)/2

now, when y=8

√x-5=8×(√30-5)/2

or, √x-5=4√30-20

or, √x=4√30-15

or, x=(4√30-15)²

or, x=47.73..

After solving the expression we get 3x² ₊ 6x ₊ 2 .

Given f(x) = 3x₊5

g(x) = 4x² ₋ 2

h(x) = x² ₋ 3x ₊ 1

f(x)  ₊  g(x) ₋ h(x)

substitute the values.

3x ₊ 5 ₊ 4x² ₋ 2 ₋ (x² ₋ 3x ₊ 1)

4x² ₊ 3x ₊ 3 ₋ x² ₊ 3x ₋ 1

3x² ₊ 6x ₊ 2

hence we get 3x² ₊ 6x ₊ 2 .

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The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.

Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab

Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.

The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.

So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.

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Answer:

19.5 ft squared

Step-by-step explanation:

Area of a triangle is (b*h)/2 so its is 39/2 or 19.5

The shapes that matches the characteristics of this quadrilateral are;

A quadrilateral is a four-sided polygon, having four edges and four corners.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.

From the given diagram of the quadrilateral we can conclude the following;

The shapes that matches the characteristics of this quadrilateral are;

Rectangle

Rhombus

Square

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Answer:

Hi I'm always here to help!!!

___________________________

x = 5

___________________________

Have a great day!!!!!!!

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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If I were required to survey Fresno City College students regarding their employment status, I would use a stratified random sampling technique.

Stratified random sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the survey. In this case, the relevant characteristic is employment status. The population consists of all Fresno City College students, and the two strata are employed and unemployed students.

Once the population has been divided into strata, a random sample is taken from each stratum. The sample size for each stratum is proportional to the size of the stratum in the population. For example, if 60% of Fresno City College students are employed, then 60% of the sample should consist of employed students.

Using a stratified random sampling technique ensures that the sample is representative of the population and that each subgroup is represented in the sample. It also reduces sampling error and increases the precision of the estimates.

Answer:

I could but can you please put down the problem.

Step-by-step explanation:

The probability of completing the test in 120 minutes or less is 0.0726, or approximately 7.26%.

P(120 < X < 150) ≈ 0.5826 - 0.0726 = 0.5100, or approximately 51.00%.

P(100 < X < 170) ≈ 0.7340 - 0.0103 = 0.7237, or approximately 72.37%.

The probability of a student not completing the test within the allotted time is 0.8499.

We expect approximately 102 students to be unable to complete the examination in the allotted time.

Probability of completing the test in 120 minutes or less:

To find this probability, we need to calculate the cumulative probability up to 120 minutes using the given mean (μ = 155) and standard deviation (σ = 24).

P(X ≤ 120) = Φ((120 - μ) / σ)

= Φ((120 - 155) / 24)

= Φ(-1.4583)

Using a standard normal distribution table or a calculator, we find that Φ(-1.4583) is approximately 0.0726.

Therefore, the probability of completing the test in 120 minutes or less is 0.0726, or approximately 7.26%.

Probability of completing the test in more than 120 minutes but less than 150 minutes:

To find this probability, we need to calculate the difference between the cumulative probabilities up to 150 minutes and up to 120 minutes.

P(120 < X < 150) = Φ((150 - μ) / σ) - Φ((120 - μ) / σ)

= Φ((150 - 155) / 24) - Φ((120 - 155) / 24)

= Φ(0.2083) - Φ(-1.4583)

Using a standard normal distribution table or a calculator, we find that Φ(0.2083) is approximately 0.5826 and Φ(-1.4583) is approximately 0.0726.

Therefore, P(120 < X < 150) ≈ 0.5826 - 0.0726 = 0.5100, or approximately 51.00%.

Probability of completing the test in more than 100 minutes but less than 170 minutes:

To find this probability, we need to calculate the difference between the cumulative probabilities up to 170 minutes and up to 100 minutes.

P(100 < X < 170) = Φ((170 - μ) / σ) - Φ((100 - μ) / σ)

= Φ((170 - 155) / 24) - Φ((100 - 155) / 24)

= Φ(0.625) - Φ(-2.2917)

Using a standard normal distribution table or a calculator, we find that Φ(0.625) is approximately 0.7340 and Φ(-2.2917) is approximately 0.0103.

Therefore, P(100 < X < 170) ≈ 0.7340 - 0.0103 = 0.7237, or approximately 72.37%.

Expected number of students unable to complete the examination:

To find the expected number of students who will be unable to complete the examination in the allotted time, we can use the properties of the normal distribution.

Let's define X as the time needed to complete the test. Given that the examination period is 180 minutes, we are interested in the probability of X exceeding 180 minutes.

P(X > 180) = 1 - Φ((180 - μ) / σ)

= 1 - Φ((180 - 155) / 24)

= 1 - Φ(1.0417)

Using a standard normal distribution table or a calculator, we find that Φ(1.0417) is approximately 0.8499.

Therefore, the probability of a student not completing the test within the allotted time is 0.8499.

Since there are 120 students, the expected number of students unable to complete the examination is:

Expected number = (Probability of not completing) * (Number of students)

= 0.8499 * 120

= 101.99

Rounding to the nearest whole number, we expect approximately 102 students to be unable to complete the examination in the allotted time.

Answer:

The probability of completing the test in 120 minutes or less is 0.0726, or approximately 7.26%.

P(120 < X < 150) ≈ 0.5826 - 0.0726 = 0.5100, or approximately 51.00%.

P(100 < X < 170) ≈ 0.7340 - 0.0103 = 0.7237, or approximately 72.37%.

The probability of a student not completing the test within the allotted time is 0.8499.

We expect approximately 102 students to be unable to complete the examination in the allotted time.

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Answer:

-2/3

Step-by-step explanation:

Answer:

d) 2p° and (p+15) ° are complementary angles.

2p° + p° + 15° = 90°

3p° = 90° - 15°

p° = 75°/3

p = 25°

Now, 2p° = 2×25° = 50°

(p+15)° = 25°+15° = 40°

e) x° and x°÷4 are supplementary angles.

x° + x°÷4 = 180°

4x + x = 180°×4

5x = 180°×4

x = 180°×4/5

x° = 36° × 4 = 144°

And x°÷4 = 144/4 = 36°

f) Complementary angles in the ratio 4:11

Let the angles be 4x and 11x .

4x + 11x = 90°

15x = 90°

x = 6°

Now, 4x = 4×6 = 24°

11x = 11×6 = 66°

g) Supplementary angles in the ratio 7:5.

Let the angles be 7x and 5x.

7x + 5x = 180°

12x = 180°

x = 180°/12

x = 15°

Hence, 7x = 7×15 = 105°

5x = 5×15 = 75°.

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:

Slope = 3

Explanation:

If we have an equation of the form

then m is the slope and b is the y-intercept.

Now in our case, the equation we have is

Here we identify m = 3. Meaning the slope of the equation is 3.

The function representing the size of the bird population is y = b(t) = 323(1.11)^(t - 3). This equation calculates the population size by starting with the initial population of 323 birds and then multiplying it by the growth factor raised to the power of (t - 3), representing the number of years since 2013.

To represent the size of the bird population over time, we can use the exponential growth model. The equation y = b(t) represents the population size, where t is the number of years since 2010.

Given that the population increases at a rate of 11% per year, we can express the growth factor as 1 + 0.11 = 1.11. This factor represents the percentage of growth for each year.

To incorporate the initial population of 323 birds in 2013, we subtract 3 from t to account for the time difference between 2010 and 2013.

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The function y = b(t) represents the size of a bird population that increases at a rate of 11% per year. In 2013, the population had 323 birds. The function relates the number of years since 2010, denoted by t, to the size of the bird population.

The function y = b(t) can be used to model the bird population size based on the number of years since 2010. Since the population increases at a rate of 11% per year, we can express the growth rate as 1 + 0.11 = 1.11.

To find the equation for the population growth, we need to consider the initial population size in 2010, denoted as b(0). Given that the population in 2013 is 323 birds, which is three years after 2010, we can set up the equation b(3) = b(0) * (1.11)^3 = 323.

By solving this equation, we can determine the value of b(0), which represents the initial bird population size in 2010. Then, the function y = b(t) can be expressed as y = b(0) * (1.11)^t.

Therefore, the function y = b(t) represents the size of the bird population, where t is the number of years since 2010, and the population increases at a rate of 11% per year.

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(A) Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

(A) Average speed = Distance / Time

Average speed = 200 meters / 19.30 seconds

Average speed = 10.36 meters per second

Therefore, Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) 1 mile = 2580 feet

Converting the distance from meters to miles:

Distance in miles = Distance in meters / (1 meter / 3.28 feet) / (1 mile / 5280 feet)

Distance in miles = 200 meters / 3.28 / 5280 miles

Time in hours = Time in seconds / (60 seconds / 1 minute) / (60 minutes / 1 hour)

Time in hours = 19.30 seconds / 60 / 60 hours

Average speed = Distance in miles / Time in hours

Average speed = (200 meters / 3.28 / 5280 miles) / (19.30 seconds / 60 / 60 hours)

Average speed = 23.35 miles per hour

Therefore, Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

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Sarah's final position would be negative. Therefore, option B is the correct answer.

Given that, Sarah starts at a positive position along the x-axis. She then undergoes a negative displacement.

A negative displacement means that Sarah has moved backward along the x-axis, so her final position would be negative.

Therefore, option B is the correct answer.

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Answer:

its attatched

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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The probability of getting an order that is not accurate or is from Restaurant C is 0.345.

The events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint events because it is possible to pick an order that is not accurate and from restaurant C (i.e., both events can occur at the same time).

The probability of getting an order that is not accurate or is from Restaurant C can be found using the addition rule of probability:

P(not accurate or from C) = P(not accurate) + P(from C) - P(not accurate and from C)

From the table, we have:

P(not accurate) = (37+50+33+16)/(315+273+248+135+37+50+33+16) = 0.170

P(from C) = 248/(315+273+248+135+37+50+33+16) = 0.209

P(not accurate and from C) = 33/(315+273+248+135+37+50+33+16) = 0.034

Therefore,

P(not accurate or from C) = 0.170 + 0.209 - 0.034 = 0.345

So, the probability of getting an order that is not accurate or is from Restaurant C is 0.345.

The events of selecting an order from Restaurant C and selecting an inaccurate order are not disjoint events because it is possible to pick an order that is both from Restaurant C and not accurate.

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Answer:

x = 14

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

48 ^2 + x^2 = 50^2

2304+x^2=2500

x^2 = 2500-2304

x^2 =196

Taking the square root of each side

sqrt(x^2) = sqrt(196)

x = 14

Answer:

14

Step-by-step explanation:

Use A^2+B^2=C^2

A=48

C=50

So B=sqrt(C^2-A^2)

B=sqrt(50^2-48^2)

B=sqrt(2500-2304)

B=sqrt(196)

B=14

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

Answer:

y=-5x-7

Step-by-step explanation:

formula: y=mx+b

(plug in numbers)

y=-5x-7

A triangle with angle measures of 90° and 125° is not possible

It is impossible for a triangle to have angle measures of 90° and 125° because the sum of the interior angles of a triangle is always 180°. In Euclidean geometry, a triangle is a closed shape with three sides and three angles.

If we have a triangle with a right angle of 90°, the sum of the other two angles must be 90° as well in order to make the total sum of angles equal to 180°. Therefore, there is no room for an angle of 125° in this triangle.

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We have the following: