Answer:
Line: I(x)= 28x+400
Step-by-step explanation:
Initial amount= $400
Interest rate= 7% simple
Total interest:
Year 1= $400+7%= 400+ 400*0.07= 400+28= 428Year 2= $400+2*7%= 400+400*0.07*2= 400+56= 456Year 3= $400+7%*3= 400+400*0.07*3= 400+84= 484Year 4= $400+7%*4= 400+400*0.7*4= 400+112= 512The graph for this function will be a line with equation:
I(x)= 400+400*0.07x= 28x+400, where I- interest, x- year
Consider the function Upper F (x )equals StartFraction f (x )Over g (x )EndFractionF(x)= f(x) g(x) with g(a)equals=0. Does F necessarily have a vertical asymptote at xequals=a? Explain your reasoning.
Answer:
No, not necessarily
Step-by-step explanation:
If g(a) = 0, it is not necessarily that F(x) will have a vertical asymptote at x = a
For instance, assume the following conditions:
[tex]F(x) = \frac{f(x)}{g(x)}\\f(x) = x^3*(x-a)\\g(x) = x-a[/tex]
In this conditions, g(a) = 0. F(a), however, can be written as:
[tex]F(x) = \frac{x^3*(x-a)}{x-a}\\F(a) = a^3[/tex]
In this particular case, F(x = a) does not show a vertical asymptote.
Jimmie invested $13,000 at 5.23% compounded monthly.
What will Jimmie's account balance be in 42 years?
Answer:
116370.197$
Step-by-step explanation:
Jimmie invested $13,000 at 5.23% compounded monthly.
Jimmie's account balance (B) after 42 years:
B = principal x (1 + rate)^time
= 13000 x (1 + (5.23/100)/12)^(42 x 12)
= 116370.197$
El perímetro de un rectángulo es 28cm, uno de los lados es 6cm más que el otro lado. Hallar el mayor lado del rectángulo.
Answer: El mayor lado del rectangulo tiene 10cm
Step-by-step explanation:
El perímetro de un rectángulo puede escribirse como:
P = 2*L + 2*A
Donde L es el largo y A es el ancho.
Sabemos que uno de los lados es 6cm mas largo que el otro, entonces podemos escribir:
L = A + 6cm.
P = 28cm = 2*L + 2*A
podemos reemplazar la primera ecuación en la segunda:
28cm = 2*(A + 6cm) + 2*A
28cm = 12cm + 4*A
28cm - 12cm = 4*A
16cm/4 = A
4cm = A.
Entonces el ancho es 4 cm, y el largo es L = 4cm + 6cm = 10cm
Un rectángulo es una figura geométrica que tiene 4 lados. Un rectángulo también se puede llamar cuadrilátero. En un rectángulo, un lado es más largo que el otro.
El lado más largo de un rectángulo se llama largo, mientras que el lado más corto se llama ancho.
El lado más largo del rectángulo (longitud) mide 10 cm.
La fórmula para el perímetro de un rectángulo se da como:
2L + 2W = P
Dónde:
P = 28cm
L = longitud
W = ancho
La pregunta dice que un lado mide 6 cm más que el otro. Esto significa que la longitud es 6 cm más que la anchura. Por lo tanto, podemos representar matemáticamente la declaración anterior:
L = W + 6
Sustituimos W + 6 por L en la fórmula
2 (W + 6) + 2W = 28
2W + 12 + 2W = 28
Recopilar términos semejantes
2 W + 2 W = 28 - 12
4W = 16
Dividir ambos lados entre 4
4W / 4 = 16/4
Ancho = 4 cm
El ancho del rectángulo es de 4 cm.
Debemos encontrar el lado más largo que es la longitud. Por eso:
L = W + 6
L = 4 + 6
L = 10 cm.
Por lo tanto, el lado más largo del rectángulo (Longitud) es de 10 cm.
Para obtener más información, visite el enlace a continuación:
https://brainly.com/question/21529866
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
What tool is used to draw circles
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
please help me with this
Answer:
Volume = 160 cm³ (Unit = cm³)
Step-by-step explanation:
Length = 4 cm
Width = 4 cm (Because it's a square based cuboid!)
Height = 10 cm
Now, Volume:
Volume = [tex]Length * Width*Height[/tex]
Volume = 4 * 4 * 10
Volume = 160 cm³
Answer:
160 cm³
Step-by-step explanation:
The base is a square. The side length of the base is 4 cm.
The volume of a square-based cuboid is the area of square × height or length.
4² × 10
16 × 10
= 160
The volume of the square-based cuboid is 160 cm³.
a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answer:
0.42
Process:
1 - 0.58
0.42
Pls help me I’ll mark brainLiest
Answer:y times 20 p
Step-by-step explanation:
One-eighth of the students in Martha's class are left handed. One-fourth of the left-handed students wear glasses. What fraction of Martha's class is left-
handed and wears glasses?
Answer:
1/32
Step-by-step explanation:
Multiply the fractions together
1/8 * 1/4 = 1/32
1/32 are left handed glass wearers
How many ways can 8 people stand in a line if Alice and Bob refuse to stand next to each other?
====================================================
Explanation:
We have 8 people to start with. If we remove Alice and Bob, and replace them with Charlie (who will be a stand in for both people), then we have 8-2+1 = 7 people in this line. There are 7! = 7*6*5*4*3*2*1 = 5040 different permutations or line orderings for these seven people.
For any given permutation, replace Charlie with Alice and Bob. There are two ways to do this for any ordering. We could have Alice in front of Bob, or Bob in front of Alice. So there are 2 times as many permutations compared to 5040. In other words, there are 2*5040 = 10,080 different permutations where Alice and Bob are standing together.
This is out of 8! = 8*7*6*5*4*3*2*1 = 40,320 different permutations overall of arranging 8 people in a line.
This means there are 40,320 - 10,080 = 30,240 different ways to arrange 8 people such that Alice and Bob are not standing together.
In summary, the idea is to find out how many ways there are to have Alice and Bob together. Then we subtract that result from the total number of ways to arrange 8 people to get our final answer.
Answer:
30240 got it from a teacher :>
Step-by-step explanation:
RSM XD
Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
Please answer this correctly
Answer:
1/7
Step-by-step explanation:
The probability of picking an even number is 3/7.
Without putting the first card back, the probability of picking an even number again is 2/6.
[tex]3/7 \times 2/6[/tex]
[tex]= 6/42[/tex]
[tex]=1/7[/tex]
Question 7
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>
The store is selling lemons at $0.43 each. Each lemon yields about 2 tablespoons of juice. How much
will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon
juice?
Answer:
$6.88
Step-by-step explanation:
16Tbs. =1 cup,
4 pies =2 cups of lemon juice, so you need 32 Tbs. of lemon juice
32/2=16
16*0.43=$6.88
Answer: $ 6.88
Step-by-step explanation:
In one cup there is 16 tablespoons.
each lemon costs .43 and gives 2 tablespoons
Half a cup would give us 8 tablespoons = 4 lemons at the cost of 1.72
1.72 times 4 pies
Making the whole thing of 4 pies cost 6.88
Giving us the answer of 6.88.
(correct me if i'm wrong)
Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?
Answer:
Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion that support the candidate has significantly changed.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=800 has a proportion of p1=0.58.
[tex]p_1=X_1/n_1=460/800=0.58[/tex]
The sample 2, of size n2=1000 has a proportion of p2=0.52.
[tex]p_2=X_2/n_2=520/1000=0.52[/tex]
The difference between proportions is (p1-p2)=0.05.
[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]
As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Han and Clare are stuffing envelopes. Han can stuff 20 envelopes in one minute, and
Clare can stuff 10 envelopes in one minute. They start working together on a pile of
1,000 envelopes. How long does it take them to finish the pile?
Answer:
33 1/2 min
Step-by-step explanation:
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
Find an equivalent ratio where the total number of students is 250
Answer: 125 boys and 125 girls = 1:1
Step-by-step explanation:
An equivalent ratio means there will be an equal number of boys and girls.
Since there are 250 students,
Boys = 250/2 = 125
Girls = 250/2 = 125
The ratio of boys to girls = 125 : 125
1 : 1 when simplified
Suppose 5 cars start at a car race. In how many ways can the top 3 cars finish the race?
The number of different top three finishes possible for this race of 5 cars is .
(Use integers for any number in the expression.)
Answer:
60 Ways
Step-by-step explanation:
We have 5 cars and have to choose 3 cars to finish the race first.
5 options for 1st car
4 options for 2nd car
3 options for 3rd car
5 · 4 · 3
Hope that helps, tell me if further explanation is needed
Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?
Hey there! :)
Answer:
x = 18 minutes.
Step-by-step explanation:
To solve this equation, set up a ratio.
# of towels over time taken:
[tex]\frac{6}{3} = \frac{36}{x}[/tex]
Cross multiply:
6x = 108
Divide both sides by 6:
6x/6 = 108/6
x = 18 minutes.
Answer:
In eighteen minutes she will have folded all 36
What is the solution to this inequality -13x> - 39
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x < 3
Interval Notation:
( − ∞ , 3 )
Answer:
x<3
Step-by-step explanation:
-13x>-39
-13x>-39 (Divided by Negative Thirteen)
-13>-13
x<3 (The great sign changes to less than when divided or multiplied by a negative number.)
x={...0,1,2}
Hope this helps ❤
Find the value of x that makes A||B
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
Help me with this please I will give you Brainliest
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
Answer:
to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]
The resulting function can be written as
[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]
Step-by-step explanation:
Hello,
f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0
and [tex]f(x)\geq 0[/tex]
so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]
and then we can write
[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]
hope this helps
I don't know if I asked this already but: 3x+2y=11 2x-2y=14 Solve for the variables.
Answer:
x = 5, y = -2.
Step-by-step explanation:
3x+2y=11
2x-2y=14
Adding removes the y terms:
5x = 25
x = 5.
Substitute for x in the first equation:
3(5) + 2y = 11
2y = 11 - 15 = -4
y = -2.
Answer:
[tex]3x + 2y = 11and2x - 2y = 14 \\ 2 \times 3x + 2 \times 2y = 2 \times 11and3 \times 2x + 3( - 2)y = 3 \times 12 \\ 6x + 4y = 22nd6x - 6y = 42 \\ 6x - 6x + 4y + 6y = 22 - 42 \\ 4y + 6y = 22 - 42 \\ 10y = 22 - 42 \\ 10y = - 20 \\ y = - 2 \\ \\ \\ \\ 2x - 2( - 2) = 14 \\ 2x + 4 = 14 \\ 2x = 10 \\ x = 5[/tex]
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps