Last week, Layla wrote 5 checks for $35 each from his checking account, withdrew another $40, and finally made a deposit of $96. What was the change in the balance of her account over the entire week

The numeric value of f(a) + f(h) for f(x) = x² - 5x + 3 is given as follows:

A. f(a) + f(h) = a² + h² - 5a - 5h + 6.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

f(x) = x² - 5x + 3.

Hence the numeric values are given as follows:

The only like term is the 3 for both expressions, hence the addition is given as follows:

f(a) + f(h) = a² + h² - 5a - 5h + 6.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Answer:

It's C) distributive property

Step-by-step explanation:

You are distributing 2 to 5 and 7

The value of the angle is 62 degrees

It is important to know the six different trigonometric identities, they are;

From the triangle shown, we have that;

The opposite side = 15

The hypotenuse side = 17

Using the sine identity, we have;

sin θ = 15/17

divide the values

sin θ = 0. 8823

take the sine invers

θ = 62 degrees

Learn about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

∠7    . However ∠7 and ∠8 are vertical angles which are equal,

Step-by-step explanation:

Angle ∠7, but because ∠7 and ∠8 are vertical angles and they are equal also.

 ∠5 corresponds to ∠7

m ∠7  = m ∠8    vertical angles are =

I will say ∠7 and ∠8.

Answer:

$450

Step-by-step explanation:

We know that the washer costs $51 more dollars than the dryer.

The washer costs x+51

The dryer costs x

So to simplify this we can do this equation:

2x+51=951

Substitute and simply the equation, and you should get this:

2x=900

x=450

Hope this helps! :)

$900

Step-by-step explanation:

if the washer and dryer combined equal 951 and the washer itself equals 51 then all you need to do is subtract to get the cost of the dryer alone.

Answer:

d. Twenty-five cars are randomly selected with the new transmission and 25 with the old transmission.

Step-by-step explanation:

A hypothesis test on the difference between the means must satisfy the following conditions

1) the samples must be randomly selected

2) each sample must have a known standard deviation

3) the samples must be independent

4) the samples must be from normal distribution

Hence only part d gives the right answer.

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

Learn more on compound interest here;

https://brainly.com/question/2455673

#SPJ1

Answer:

Step-by-step explanation:

If 11 flights were sampled with an 85% on-time arrival rate, the number of flights from the sample that arrived on time would be estimated to be 9.35, which would round to 9 flights.

This can be solved by:

(0.85x11)= 9.35

Since there can't be .35 of a flight, we would round to the nearest whole number, which would just be 9.

The final answer= 9 flights

Step-by-step explanation:

To calculate the amount of money in the account at the end of 4 years, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal amount (initial deposit)

r = Annual interest rate (as a decimal)

t = Time period (in years)

Plugging in the given values, we get:

I = $50,000 * 0.025 * 4

I = $5,000

This means that over the course of 4 years, the account will earn $5,000 in interest.

To find the total amount in the account at the end of 4 years, we simply add the interest earned to the initial deposit:

Total amount = $50,000 + $5,000

Total amount = $55,000

Therefore, at the end of 4 years, there will be $55,000 in the account if you deposit $50,000 into a bank account that earns 2.5% simple interest annually.

Answer:

5

Step-by-step explanation:

(because when two negative meets it gives u positive )

The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.

What is meant by pedagogical tool?

In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.

Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.

While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.

To know more about pedagogical tool here.

https://brainly.com/question/22211984

#SPJ4

Answer:

f(3)=5

Or

(3,5)

Step-by-step explanation:

all you have to do is look at what y axis is on the line when x=3

And y=5

f(3)=5

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

Answer: $507.66

Step-by-step explanation:

408.68 + 98.98 = 507.66

Answer:

For the first question the answer is A- 1, 440. For the second question the answer is C- $3,000.

Step-by-step explanation:

For question 1 I got 1,440 because 8 x 12 = 96 and 112 x 12 equaled 1344 so when I added those two up I got 1,440.

For question2 I got, $3,000 because 16 x 125 = 2000 + 1000 so the answer to that question is $3000.

Answer:

\(\large \boxed{ \sf Height= 117.78 \ m }\)

Step-by-step explanation:

We need to find out the height of the skyscraper to thr nearest hundred of metre .

D I A G R A M : -

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,0){4}}\put(0,0.001){\line(0,1){1.5}}\put(0,1.5){\line(2,1){4}}\put(4,0){\line(0,1){3.5}}\put(0,1.501){\line(1,0){4}}\multiput(-1,0.75)(5.1,0){2}{$\sf 1.75 m $}\multiput(2,-0.75)(0,2.5){2}{$\sf 337 m $}\put(4.5,2.2){$\sf x $}\qbezier(0.7,1.5)(0.7,1.7)(0.5,1.75)\put(1,1.67){$\sf 19^\circ $}\put(5,-1.5){$\textcopyright \bf TonyStark $}\put(4, - .5){$\sf C $} \put(4,3.7){$\sf A $} \put(4.1,1.5){$\sf B $} \put( - .5,1.5){$\sf D $} \end{picture} \)

Here we can make use of trigonometric ratios to find out the value of firstly AB . In a right angled triangle, tangent is defined as the ratio of perpendicular and base. With respect to angle 19° , the perpendicular is "x" and the base is 337m.

Now in ∆ABD , we have ;

\(:\implies\sf tan\theta =\dfrac{AB}{BD}\\\)

\(:\implies\sf tan 19^\circ =\dfrac{ x}{337\ m} \\\)

\(:\implies\sf 0.3443=\dfrac{x}{337m} \\\)

\(:\implies\sf x = 337m \times 0.3443 \\\)

\(:\implies\sf \pink{ x =\frak{ 116.03 \ m }} \\\)

Now the total height of the skyscraper will be the sum of BC and AB , therefore;

\(:\implies\sf height_{skyscraper}= AB + BC \\\)

here ,

\(:\implies\sf Height_{skyscraper}= (116.03 + 1.75) m\\\)

\(:\implies\sf \underline{\underline{\boxed{ \sf Height_{skyscraper}= \frak{117.78\ m }}}} \\\)

Hence the height of the skyscraper is 117.78 m .

Answer:

The height of the skyscraper is 117.79 m to the nearest hundredth.

Step-by-step explanation:

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find the height of the building, model as a right triangle and solve using the tangent trigonometric ratio. (See the attached diagram).

Tan trigonometric ratio

\(\tan \theta=\sf \dfrac{O}{A}\)

where:

Given information:

The line of sight is 1.75 m above ground level.  Therefore, the height of the skyscraper (the side opposite the angle of elevation) is (y + 1.75) m.

To find y, substitute θ = 19°, O = y and A = 337 into the tan ratio:

\(\implies \tan 19^{\circ}=\dfrac{y}{337}\)

\(\implies y=337 \tan 19^{\circ}\)

\(\implies y=116.038405...\)

To calculate the height of the skyscraper, add the found value of y to 1.75 m:

\(\begin{aligned}\implies \sf Height\;of\;skyscraper&=y+1.75\\&=116.038405... + 1.75\\&= 117.78840...\\&=117.79\; \sf m\;(nearest\;hundredth)\end{aligned}\)

Therefore, the height of the skyscraper is 117.79 m to the nearest hundredth.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

-4x+4y+3=0

Step-by-step explanation:

(4x-2y+9=0)+(-8x+6y-6=0)

Add like terms:

-4x+4y+3=0

Answer:

False

Generally speaking it is better to cash a check at the bank you use where the money will be deposited. Doing this is the best ways to avoid transaction fees, handling fees, or any other extra fees

The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

To know more about hypotenuse:

https://brainly.com/question/12006293

#SPJ1

Answer: 8 books

Step-by-step explanation:

y= how much shelf space take up (inches)

x= # of books

y=2x

in this situation 16=y

16=2x

divide both sides by 2

8=x

The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

To learn more about Lagrange multipliers , visit the link:

https://brainly.com/question/30459783

#SPJ1

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}\)

Answer:

c

Step-by-step explanation:

Since area is lw  3*3=9

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

Answer:

it is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

sinx=12/54

x=arcsin(12/54)

x=12.84 degrees (rounded to nearest hundredth of a degree)

Answer:

I don't know what to do with it but I don't

Step-by-step explanation:

hahahaha