Answer:
72%
Step-by-step explanation:
68% + x/2 = 70%
68 + x = 140
x = 72
In investing $6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $428. How much money was invested at each rate?
Answer:
$ 2,600 was invested at 4% and $ 3,600 was invested at 9%.
Step-by-step explanation:
Given that in investing $ 6,200 of a couple's money, a financial planner put some of it into a savings account paying 4% annual simple interest, and the rest was invested in a riskier mini-mall development plan paying 9% annual simple interest, and the combined interest earned for the first year was $ 428, to determine how much money was invested at each rate, the following calculation must be performed:
3000 x 0.04 + 3200 x 0.09 = 408
2500 x 0.04 + 3700 x 0.09 = 433
2600 x 0.04 + 3600 x 0.09 = 428
Therefore, $ 2,600 was invested at 4% and $ 3,600 was invested at 9%.
What are the x-intercepts of this quadratic function?
g(x) = -2(x - 4)(x + 1)
Answer:
4 and -1
Step-by-step explanation:
A quadratic function is given to us and we need to find the x Intercepts of the given function . The function is ,
[tex]\bf \implies g(x) = -2( x -4)(x+1)[/tex]
Step 1 : Equate the function with 0,
[tex]\bf \implies -2( x -4)(x+1) = 0 [/tex]
Step 2: Equating with 0 :-
Now equate each factors seperately with 0 , to get the x Intercepts.
Step 3: Finding the intercepts :-
[tex]\bf \implies x - 4 = 0 \\\\\implies\boxed{\bf\blue{ x = 4 }} [/tex]
Again ,
[tex]\bf \implies x + 1 = 0 \\\\\implies\boxed{ \blue{\bf x = -1}} [/tex]
Hence the x intercepts are 4 and -1 .
Answer:D (4,0) and (-1,0)
Step-by-step explanation:
4. As part of your retirement planning, you purchase an annuity that pays 4 % annual
interest compounded quarterly
a. If you make quarterly payments of $900 how much will you have saved in 5
years?
b. Instead, if you make quarterly payments of $450, how much will you have saved
in 10 years?
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Answer:
a. $19817.10
b. $21998.87
Step-by-step explanation:
The formula for the future value of an annuity with payments "A" and interest at rate r compounded quarterly for t years is ...
FV = A((1 +r/4)^(4t) -1)/(r/4)
The attachment shows this evaluated for ...
a. A = 900, r = 0.04, t = 5. FV = $19817.10
b. A = 450, r - 0.04, t = 10. FV = 21,998.87
a family has two children. what is the probability that both are girls, given that at least one is a boy
Answer: The probability would be zero
Step-by-step explanation:
There are two children and one is a boy, so the probability of both being girls is a zero
Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).
Then draw the graph of g(x).
1. g(x) = f(x + 1)
2. g(x) = f(x) - 2
Please help i also need to graph
9514 1404 393
Answer:
left 1 unitdown 2 unitsStep-by-step explanation:
The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.
1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)
__
2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)
Diane bought new headphones originally listed for $70.99. They are 25% off. Which equation can be used to find the amount Diane will save?
Step-by-step explanation:
100% = $70.99
there is a discount of 25%.
that means 75% (100 - 25) of the original price remains.
the equation to get any x% amount of a 100% total is simply
x% amount = 100% total amount × x/100
25% = 70.99 × 25/100 = $17.75
If 12x + 16y = 11, what is the value of 6x + 8y?
Answer:
11/2
Step-by-step explanation:
Given 12x+16y=11
Halving both sides gives 6x+8y=11/2.
A line has a slope of -5 and
passes through the point
(0, -7). What is its equation in
slope-intercept form?
Write your answer using integers,
proper fractions, and improper
fractions in simplest form.
A store sells 5 different shirts, 6 different pants, 3 different shoes, and 9 different socks. You are making an outfit with one of each article of clothing. How many outfits can you make?
Answer:
you can make 3 outfits
Step-by-step explanation:
because,if you just have 3 shoes aotomaticly you just wear 3 shirt and 3 pants.
for the socks, one people wear 2 socks so there you have 3 outfits
Answer:
[tex]810[/tex]
Step-by-step explanation:
For each shirt, there are 6 different pairs of pants to pair with it. For each of these pairs of pants, there are 3 different shoes to pair and so on.
Therefore, there are [tex]5\cdot 6\cdot 3\cdot 9=\boxed{810}[/tex] combinations you can make.
X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b?
a perfect square trinomial, (x + y)² = x² + 2xy + y²
so, if we have the x of the bx, what is left is the b
the expression would have to be (x + 7)², since we have the 49 and the x²
so, what's left: x² + 14x + 49,
b = 14
hope it helps :)
Solve 3x to the second power +17x-6=0
The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The quadratic equation is,
⇒ 3x² + 17x - 6 = 0
Now, We can solve the equation as;
⇒ 3x² + 17x - 6 = 0
⇒ 3x² + (18 - 1)x - 6 = 0
⇒ 3x² + 18x - x - 6 = 0
⇒ 3x (x + 6) - 1 (x + 6) = 0
⇒ (3x - 1) (x + 6) = 0
This gives two solutions,
⇒ 3x - 1 = 0
⇒ x = 1/3
And, x + 6 = 0
⇒ x = - 6
Learn more about the quadratic equation visit:
brainly.com/question/1214333
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Now suppose that not every player can play in every position. The outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch. Suppose a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers.
How many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled?
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
A student writes
2
pages of a report in
2
an hour. What is her unit
rate in pages per hour?
Answer:
1 page of a report per hour
Step-by-step explanation:
2/2= 1 page per hour
Lets find unit rate
[tex]\\ \sf\longmapsto \dfrac{2\dfrac{1}{2}}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{2}\div 2[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{4}[/tex]
[tex]\\ \sf\longmapsto 1.2pages/hour[/tex]
Find the value of x in each case:
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Answer:
x = 36
Step-by-step explanation:
The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...
(180 -2x) +x +(180 -4x) = 180
180 = 5x . . . . . . add 5x-180 to both sides
36 = x . . . . . . . divide by 5
__
Additional comment
This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.
Convert 333 to base three.
Answer:
110100
Step-by-step explanation:
44 and 45 are alternate interior
angles. Find the measure of 44.
t
115/65°
43/44
44 = [?]
t
45/46
47/48
274
Fnter
Answer:
115
Step-by-step explanation:
The opposite angles (115degree angle and angle 4) are equal.
Angle 3=65
Angle 4=115
Angle 5=115
Angle 6=65
Angle 7=65
Angle 8=115
Brainliest please~
Which of the following numbers is rational? Assume that the decimal patterns continue.
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Answer:
(c) √49
(d) 2.544544...(3-digit repeat)
Step-by-step explanation:
Square roots of perfect squares are rational, as are repeating decimals.
The radius of a circular disk is given as 26 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error
Answer:
(a) Hence the maximum error in the calculated area of the disk is 32.67[tex]cm^{2}[/tex].
(b) Hence the relative error is 1.54%.
Step-by-step explanation:
Here the given are,
The Radius of the circle r = 26cm.
The maximum error in measurement dr = 0.2 cm.
Answer:
(a) [tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) [tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
Step-by-step explanation:
radius, r = 26 cm
error = 0.2 cm
(a) The area of the disc is given by
[tex]A = \pi r^2\\\\dA = 2\pi r dr\\\\dA = 2 \times 3.14\times 26\times 0.2= 32.66[/tex]
Now
A = 3.14 x r x r = 3.14 x 26 x 26 = 4245.28 cm^2
So, the area with error is given by
[tex]A =(4245.28\pm32.66) cm^2[/tex]
(b) The relative error is
[tex]\frac{dA}{A}=\frac{32.66}{4245.28}=0.0077[/tex]
x to the power of 3 - 7x + 6 factorise please whole step by step
Answer:
[tex](x + 3)(x - 2)(x - 1)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 7x + 6[/tex]
Factor using Rational Root Theorem.
This means our possible roots are
positve or negative (1,2,3,6). If we try positve 1, it is indeed a root.
This means that
[tex](x - 1)[/tex]
is a root.
We can divide the top equation by the root (x-1). Our new equation is
[tex]( {x}^{2} + x - 6)[/tex]
Now we can factor this completely
[tex](x + 3)(x - 2)[/tex]
So this equation in factored form is
[tex](x + 3)(x - 2)(x - 1)[/tex]
Do 8 plz find OS thanks
Answer:
OS = 10
Step-by-step explanation:
We can use a ratio to solve
QP PR
----- = ------
QO OS
14 7
----- = -------
14+6 OS
14 7
----- = -------
20 OS
Using cross products
14 * OS = 7*20
14 OS = 140
Divide by 14
OS = 140/14
OS = 10
14) The height, h metres, of a ball projected directly upwards from the ground can be modelled by h = 56t - 71, where t is the time in seconds after it leaves the ground. a) Find the height of the ball 3.5 seconds after it leaves the ground. b) At what time will the ball strike the ground again? c) When will the ball be 49 m above the ground? Briefly explain why there are two possible answers.
A jar of gumballs contains 4 reds, 2 greens, and 6 blues. What is the probability of getting two blues in a row without replacement?
Select one:
a. 3/4
b. 1/2
c. 5/22
d. 5/11
Answer:
C
Step-by-step explanation:
Hypergeometric distribution
[tex]\frac{{6\choose2}}{{12\choose2}}=\frac{15}{66}= \frac{5}{22}[/tex]
A kite is a quadrilateral with two pairs of adjacent, congruent sides. The vertex angles are those angles in between the pairs of congruent sides. Prove the diagonal connecting these vertex angles is perpendicular to the diagonal connecting the non-vertex angles. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Will give brainliest answer
Answer:
Step-by-step explanation:
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
The solutions of this system of equation is (-5,3) and (-1,-5).
Answer: (-3,-1) and (-5,3)
Step-by-step explanation:
Which equation is equivalent to 15-7x=14
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{15 - 7x = 14}[/tex]
[tex]\large\text{-7x + 15 = 14}[/tex]
[tex]\underline{\large\text{SUBTRACT 15 to BOTH SIDES}}[/tex]
[tex]\large\text{-7x + 15 - 15 = 14 - 15}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: 15 - 15 because that gives you 0}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: 14 - 15 because that helps solve for the x-value}}}[/tex]
[tex]\large\text{14 - 15 = \bf -1}[/tex]
[tex]\underline{\underline{\underline{\large\text{NEW EQUATION: -7x = -1}}}}[/tex]
[tex]\underline{\large\text{DIVIDE -7 to BOTH SIDES}}[/tex]
[tex]\mathsf{\dfrac{-7\mathsf{x}}{-7}=\dfrac{-1}{-7}}[/tex]
[tex]\underline{\underline{\large\text{CANCEL out: } \dfrac{-7}{-7} \large\text{ because that gives you 1}}}[/tex]
[tex]\underline{\underline{\large\text{KEEP: }\dfrac{-1}{-7}\large\text{ because helps you get the x-value}}}[/tex]
[tex]\mathsf{x = \dfrac{-1}{-7}}[/tex]
[tex]\mathsf{x = \dfrac{-1\div-1}{-7\div-1}}[/tex]
[tex]\mathsf{x =\bf \dfrac{1}{7}}[/tex]
[tex]\boxed{\boxed{\large\text{Therefore, your answer is: \bf x = }\bf \dfrac{1}{7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
what is the length of AB? round to one decimal place
Answer:
A=0
Step-by-step explanation:
DAC=BAD
A=0
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
Find the fourth proportion to : 2,3,16
Answer is 24
Step by step:
2,3,16
Let the fourth proportion be x
2/3 = 16/x
or, 2x = 3×16
or, x = 3×16/2
or, x = 3×8
or, X = 24
what is the area of a triangle of base 10m and height of 8m
Answer:
40m
Step-by-step explanation:
to find the area of a triangle you must do bh/2
So you do 10 times 8 which is 80.
Then you do 80 divided by 2 which is 40.
I hope this helps!