You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.
a. Write an exponential equation to determine when the balance of the account will be $1500
b. Solve the equation.

The cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.

According to the questions,

4 kilograms of almonds cost $34. In order to find one kilograms of almonds  only if we divide 34 by 4.

= [tex]\frac{34}{4}[/tex] = 8.5

Hence, the cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.

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The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks

What is share buyback?

Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.

The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.

The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.

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The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.

The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU  and side ST must be proportional to side UT

Hence, RS/VU=ST/UT.

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The definition of the piecewise function is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:

y = x + b

0 = -3 + b

b = 3

Then:

[tex]f(x) = x + 3, -3 \leq x < 1[/tex].

For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:

[tex]f(x) = 5, -1 \leq x \leq 1[/tex].

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Answer: 4

Step-by-step explanation:

Slope is rise over run (up over sideways) from two points.

The two points shown are (0,4) and (-2,-4).

By counting, you can find the slope, which is 8/2 = 4.

Answer:

10 units

Step-by-step explanation:

the longest length is from (11, 1) to (3, 7) and can be clearly shown when graphed

now to find the length you must use the pythagorean theorem

the distance between 11 and 3 is 8 and the distance between 1 and 7 is 6 so

8^2 + 6^2 = c^2

64 + 36 = c^2

100 = c^2

c = 10

that is your answer

Answer:

C. Best models this relationship

Step-by-step explanation:



Answer:

C: y=1/3x

Step-by-step explanation:

I'll set up an equation for this.

When x = 6, y needs to be 2.

--> 2 = 6 times ___

since 6 times 1/3 is 2, ___ is 1/3.

Now we know that 1/3 is the slope. In a complete equation, this will be shown as y = 1/3 x.

This can be proven by reinserting the value of x and y.

2 = 1/3 (6)

Since this equation works, we can be sure that C: y=1/3 x is correct.

All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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Answer:

9

Step-by-step explanation:

Let x = # of movies Jamie watches in a month. 5 + 2.25x represents the monthly cost of Amazing Primo, and 15 + x represents the monthly cost of Netflakes.

5 + 2.25x > 15 + x

1.25x > 10

x > 8

Jamie must watch more than 8 movies each month for the Netflakes account to be cheaper overall.

Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.

Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.

That is, perpendicular bisector PQ of line segment AB is the line with         Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.

Thus in the given question we can use perpendicular bisector theorem.

Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.

Hence it is clear that Option A is correct.

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Answer:

[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

The number is 2.

Step-by-step explanation:

The reciprocal of a number is simply 1 divided by the number.

The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).

Let x be the positive number.

The reciprocal of the positive number x:

[tex]\sf \implies \dfrac{1}{x}[/tex]

The reciprocal of 3 more than the number x:

[tex]\sf \implies \dfrac{1}{x+3}[/tex]

The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:

[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]

To solve, make the denominators of the two fractions on the left side the same by multiplying them.

Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.

Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.

[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]

[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]

Add the numerators and keep the denominator so that there is now one fraction:

[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]

Cross multiply:

[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]

Expand:

[tex]\implies \sf 20x+30=7x^2+21x[/tex]

Rearrange so the equation is equal to zero:

[tex]\implies \sf 7x^2+x-30=0[/tex]

Split the middle term:

[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]

Factor the first two terms and last two terms separately:

[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]

Factor out the common term (7x + 15):

[tex]\implies \sf (x-2)(7x+15)=0[/tex]

Apply the zero product property:

[tex]\sf (x-2)=0 \implies x=2[/tex]

[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]

As x is a positive number, x = 2.

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The length of the side of the octagon is 4.142 inches.

Let the length of the congruent sides of the isosceles triangle be x.

The hypotenuse of the triangle is given by:

√x+x = √2x

This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.

It is also given that the length of the square side is 10 inches.

This means that:

x + √2x + x = 10

2x + √2x = 10

(2 + √2)x = 10

(2 + 1.414)x = 10

3.414x = 10

x = 10/3.414

x = 2.929 inches.

The side of the octagon is given by:

√2 × 2.929 = 4.142 inches

Therefore, we have found that the length of the sides of the octagon is 4.142 inches.

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Hello !

[tex](x {}^{a} ) {}^{b} = x {}^{a \times b} [/tex]

[tex](b {}^{5} ) {}^{2} = b {}^{ 5\times 2} = b {}^{10} [/tex]

→ Answer D

Answer:

D

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](b^5)^{2}[/tex] = [tex]b^{5(2)}[/tex] = [tex]b^{10}[/tex]

Answer: [tex]m\angle 1=82^{\circ}, m\angle 2=128^{\circ}[/tex]

Step-by-step explanation:

By the same-side interior angles theorem,

[tex]m\angle 1=180^{\circ}-98^{\circ}=82^{\circ}\\\\m\angle 2=180^{\circ}-52^{\circ}=128^{\circ}[/tex]

If you select 25 in the Top Values list, Access displays the top 25 records in the query results.

Queries are excellent tools in Microsoft Excel to show information from related tables in a single result set, as the results that you pull from queries aren’t limited to a single table.

The way to create a simple query using the wizard is as follows;

Now, If you select 25 in the top values list, access displays the top 25 records in the query results.

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The probability that Ron will get by a pitch exactly once is 0.351912.

Given that out of 596 plate appearance Ron was hit 19 times from pitches.

We have to find the probability that ron was hit by pitches in 22 plate appearances.

The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.

We can find the required probability through binomial distribution which is

n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.

Probability that Ron will be hit =19/596

=0.031

Probability that Ron will get hit by a pitch exactly once =P(X=1)

=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]

=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]

=22*0.031*0.516

=22*0.015996

=0.351912

Hence the probability that Ron will get hit by a pitch exactly once is 0.35.

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Answer:

1. The zeros are at x = 0 and x = –10

2. The zeros are at x = 3 and x = 4

Step-by-step explanation:

1. f(x) = x (x + 10)

Multiplying any number by 0 = 0,
so f(x) = 0 when...

• x = 0

or

• x + 10 = 0 (if you subtract 10 from both sides, you get x = –10)

2. f(x) = x (x - 3) – 4 (x - 3)

Use distributive property to expand

x² – 3x – 4x + 12

Combine like terms

x² – 7x + 12

Factor

(x – 3) (x – 4)

(You could have also just noticed in the original function that both x and –4 were multiplied by (x – 3) and factored then.)

So f(x) = 0 when...

• x – 3 = 0  (add 3 to both sides to get x = 3)

or

• x – 4 = 0 (add 4 to both sides to get x = 4)

I hope that helped!

The modal and mean mark of the frequency distribution is 5 and 4.83 respectively.

Mode refers to a mark which reoccurs most in a frequency distribution.

The total number of students who wrote the test = 2 + 3 + 4 + 6 + 10 + 4 + 3 + 2 + 1 + 1

= 36 students

Mean mark = Total mark / Total students

= (2×1) + (3×2) + (4×3) + (6×4) + (10×5) + (4×6) + (3×7) + (2×8) + (1×9) + (1×10) / 36

= (2+6+12+24+50+24+21+16+9+10 / 36

= 174/36

= 4.83333333333333

Approximately,

Mean mark = 4.83

If 25% of students failed,

Number of students who failed = 25% of 36

= 25/100 × 36

= 0.25 × 36

= 9 students.

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The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

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a. circle 2 = 60°

circle 3 = 120°

circle 4 = 180°

circle 5 = 240°

circle 6 = 300°

b. circle 8 = 15°

circle 9 = 75°

circle 10 = 155°

circle 11 =  215°

circle 12 =  265°

From the information given, we have that;

There are six major circles

Six minor circles

a. There are 6 circles at a point

Note that angles at a point sum up to 360 degrees

Now, let's divide their sum by the six parts

= [tex]\frac{360}{6}[/tex]

= [tex]60[/tex] degrees

Then, circle 1

= 0 × 60

= 0

Circle 2

=  1 × 60

=  60°

Circle 3

= 2 × 60

= 120°

Circle 4

= 3 × 60

= 180°

Circle 5

= 4 × 60

= 240°

Circle 6

= 5 × 60

= 300°

b. We have that each of these circles ( circle 7 - 12) radian measure is

= main circle - [tex]\frac{\pi }{12}[/tex]

The relative position or direction of circle 7 - 12 to their corresponding main circles ( 1 - 6) are all the same, we then have;
For circles 8

= 60° - 45°

= 15°

Circle 9

= 120° - 45°

= 75°

Circle 10

= 180° - 45°

= 155°

Circle 11

= 240° - 45°

= 215°

Circle 12

= 300° - 45°

= 265°

They share the relationship of radian of circle 7 - 12 corresponding to circles 6 - 12 minus π/12

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The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

Given the nth term of a recursive expression shown below

an =an-1 - 1.4

where

an-1 is the preceding term

a1 is the first term

an is the nth term

an-1 is

Given the following

a1 = 0

For the second term a2

a2 = 0 - 1.4

a2 = -1.4

For the third term a3

a3 = -1.4 - 1.4

a3 = -2.8

For the fourth term a4

a4 = -2.8 - 1.4

a4 = -4.2

For the fifth term a2

a5 = -4.2 - 1.4

a5 = -5.6

Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}

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Answer:

45 numbers

Step-by-step explanation:

The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.

Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit

30-39 ~ 30, 31, 32 follow the property

40-49 ~ 40, 41, 42, 43 follow the property

We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:

50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers

We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:

1+2+3+4+5+6+7+8+9=45

Answer:

28, 4 or 4, 28 (order doesn't matter, both are true answers)

Step-by-step explanation:

l + w = 32

l*w = 112

l = 112/w

112/w + w = 32

w = 28 or 4

l = 28 or 4

Answer:

4,28

Step-by-step explanation:

So let's look at the sentence to take any necessary information out. It says the length of a rectangle plus it's width is 32. Since we do not know what the length and width are, let's just represent them as L (length) and W (width). Using this information we get the equation: [tex]L + W = 32[/tex] and since we're given the area of the rectangle, we can also define another equation which is: [tex]LW = 112[/tex] since the length * width = area.

So now all we have is a systems of equations. We can solve for L or W in the area equation and plug it into the addition equation. We can also solve for L or W in the addition equation and then plug it into the area equation, either should work, but in this example I'll solve for L in the addition equation:

Original Equation:

[tex]L + W = 32[/tex]

Subtract 32 from both sides

[tex]L = 32-W[/tex]

Now let's use this definition of L to plug into the second equation:

[tex]LW = 112 \implies (32-W)W = 112[/tex]

Distribute the W

[tex]-W^2+32W=112[/tex]

Now if you notice, we simply have a quadratic equation and we can subtract 112 from both sides and then use the quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Subtract 112 from both sides

[tex]-W^2+32W-112=0[/tex]

Use quadratic formula

[tex]W = \frac{-32\pm\sqrt{32^2-4(-1)(-112)}}{2(-1)}[/tex]

Simplify stuff in radical

[tex]W = \frac{-32\pm\sqrt{576}}{-2}[/tex]

Calculate the square root

[tex]W=\frac{-32\pm24}{-2}[/tex]

Use positive sign:

[tex]W=\frac{-32+24}{-2}[/tex]

Simplify numerator

[tex]W = \frac{-8}{-2}[/tex]

Simplify fraction

[tex]W=4[/tex]

Take negative sign
[tex]W = \frac{-32-24}{-2}[/tex]

Simplify numerator

[tex]W=\frac{-56}{-2}[/tex]

W = [tex]28[/tex]

So we have two solutions, and the reason for this is because had we solved for W in the original equation and substituted that into here, there would be no different, it's not bound by some variable name. So these are actually the two sides of the rectangles

4 + 28 = 32

4 * 28 = 112

4, 28

Answer:

925.5

Step-by-step explanation:

Hope it helps!

<3

The surface area of the parallelpiped is equal to 800 square units.

The surface area of the parallelpiped seen in the picture is equal to the sum of the areas of its six faces, which are combination of areas of quadrilaterals and triangles. There are four parallelograms and two squares. Thus, the surface area of the solid is:

A = 2 · 8 · 20 + 2 · 7 · 20 + 2 · 10²

A = 800

The surface area of the parallelpiped is equal to 800 square units.

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Considerando la definición de una ecuación, el número desconocido es 50.

Una ecuación es la igualdad existente entre dos expresiones algebraicas conectadas a través del signo de igualdad en la que figuran uno o varios valores desconocidos, llamadas incógnitas, además de ciertos datos conocidos.

Los miembros de una ecuación son cada una de las expresiones que aparecen a ambos lados del signo igual.

En este caso, "La suma de un número con su mitad es igual a 75" puede ser expresado mediante una ecuación, donde consideras que "x" es la incógnita, que representa el número desconocido.

Teniendo en cuenta que la mitad de un número se calcula dividiendo el número por 2, entonces la ecuación queda expresada como:

x + x÷2= 75

O lo que es lo mismo

x + [tex]\frac{1}{2}[/tex]x= 75

Resolviendo:

[tex]\frac{3}{2}[/tex]x= 75

x= 75 ÷[tex]\frac{3}{2}[/tex]

x= 75×[tex]\frac{2}{3}[/tex]

x=50

Finalmente, el número desconocido es 50.

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Using a system of equations, it is found that she earns $5.5 for each hat and $7 for each scarf sold.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

One week she earns $114.00 by selling eight hats and 10 scarves, hence:

8x + 10y = 114.

The following week she sold 12 hats and six scarves and earned $108.00, hence:

12x + 6y = 108

Simplifying by 6:

2x + y = 18

y = 18 - 2x.

Replacing in the first equation:

8x + 10y = 114.

8x + 10(18 - 2x) = 114

12x = 66

x = 66/12

x = 5.5

y = 18 - 2x = 18 - 2 x 5.5 = 7.

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