$2212.93 should be invested
Explanations:Let the amount to be invested be the principal, P.
The interest rate, r = 4.9%
r = 4.9/100
r = 0.049
Time, t = 10 months
12 months = 1 year
10 months = 10/12
t = 10/12 years
t = 0.83
The interest in the next 10 months, I = $90
Interest, I, is given by the formula:
I = P x r x t
90 = P x 0.049 x 0.83
90 = P x 0.04067
P = 90 / 0.04067
P = $2212.93
How do I find the point slope intercept of a line
for the slope, the equation is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]in case you have two points
The equation of the line equation:
[tex]y=mx+b[/tex]If you want to find the interception in x-axis, you have to change the y for a 0, like this
[tex]0=mx+b[/tex][tex]x=-\frac{b}{m}[/tex]If you want to find the interception in y-axis, you have to change the x for a 0, like this, that is "b" in the equation
[tex]y=m(0)+b[/tex][tex]y=b[/tex]I need help with this
A trinomial is a polynomial that has three terms.
Let the unknown trinomial be represented by A
Thus, the difference between the two trinomials as stated in the question will be represented mathematically as;
[tex]\begin{gathered} A-(3x^2-2x+7)=5x^2+11x-16 \\ \text{Making A the subject of the formula, we have} \\ A=(5x^2+11x-16)+(3x^2-2x+7) \\ \operatorname{Re}\text{arranging and collecting the like terms, we have;} \\ A=5x^2+3x^2+11x-2x-16+7 \\ A=8x^2+9x-9 \end{gathered}[/tex]Therefore, the expression of the other trinomial is;
[tex]A=8x^2+9x-9[/tex]The correct answer is option C.
6 in. SA = 2ten2 + 2trh (Use 3.14 for a.) Find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches. square inches 8 in. Do NOT round your answer.
207.24 in²
1) Gathering the data
height: 8"
Base Diameter: 6" then a Radius: 3 for D=2R
2) Let's find the Surface Area from this Cylinder by plugging into that the given data:
[tex]\begin{gathered} SA=2\pi\cdot r^2+2\pi rh \\ S_A=2(3.14)\cdot(3)^2+2\cdot3.14\cdot3\cdot8 \\ S_A=207.24in^2 \end{gathered}[/tex]3) Hence, the answer is 207.24 in²
Solve using substitution. 6x + y = 5 -8x - 5y = 19 how do I do this
The given system of equations is
[tex]\begin{gathered} 6x+y=5 \\ -8x-5y=19 \end{gathered}[/tex]To solve the system, first, let's multiply the first equation by 5.
[tex]\begin{gathered} 30x+5y=25 \\ -8x-5y=19 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} 30x-8x+5y-5y=25+19 \\ 22x=44 \\ x=\frac{44}{22} \\ x=2 \end{gathered}[/tex]Now, we find y
[tex]\begin{gathered} 6x+y=5 \\ 6\cdot2+y=5 \\ 8+y=5 \\ y=5-8 \\ y=-3 \end{gathered}[/tex]Hence, the solution is (2,-3).Use the fundamental identities to find the value of trigonometric function. Find csc θ, given that sin 2θ = - — and θ is in quadrant IV. 3
Recall that:
[tex]\csc \theta=\frac{1}{\sin\theta}\text{.}[/tex]If:
[tex]\sin \theta=-\frac{2}{3},[/tex]then:
[tex]\csc \theta=\frac{1}{-\frac{2}{3}}\text{.}[/tex]Simplifying the above result we get:
[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]Answer:
[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]Dominic has a bag of candy full of 1 strawberry chew and 19 cherrychews that he eats one at a time. Which word or phrase describes theprobability that he reaches in without looking and pulls out a lemonchew?A.certainB.unlikelyC.likelyD.impossible
D.impossible
there is no Lemon chew, only strawberry chew and cherry chews
I need help I’ve been having trouble with this chapter for about a week
Given:
[tex]3x^2+20x+33[/tex]Find-:
Factorization of the equation.
Sol:
A simple method of factorization is to multiply in first and last order then break it down into parts to make the middle number then.
[tex]\begin{gathered} =3\times33 \\ =99 \end{gathered}[/tex]
The factor of 99 is:
So take factor :
[tex]\begin{gathered} 11\text{ and \lparen3}\times3) \\ \\ 11\text{ and 9} \end{gathered}[/tex]Factorization of the equation is:
[tex]\begin{gathered} =3x^2+20x+33 \\ \\ =3x^2+11x+9x+33 \end{gathered}[/tex]a card is drawn at random from a standard deck. Determine whether the events are mutually exclusive or not mutually exclusive. Then find each probability. P(jack or 4)
Mutually exclusive events:
Two events are mutually exclusive if they cannot occur at the same time.
There are 52 cards in a deck of cards.
n(s)=52.
Let A be event of getting jack.
n(A)=4.
So, Probability of getting jack is,
Let B be event of getting 4
n(B)=4.
So, Probability of getting 4 is,
[tex]\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{4}{52} \end{gathered}[/tex]These two events do not occur at same time.
Therefore the events are mutually exclusive.
[tex]P(A\cap B)=0[/tex]To find the probability of getting jack or 4
[tex]P(\text{A }\cup\text{B)}=P(A)+P(B)-P(A\cap B)[/tex]hence,
[tex]\begin{gathered} P(\text{A }\cup\text{B)}=\frac{4}{52}+\frac{4}{52}-0 \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The probability of getting jack or 4 is,
[tex]\frac{2}{13}[/tex]Determine the initial investment, PV, for a future value of 6500 dollars if the nominal rate of interest is 5.9 percent compounded quarterly for 12 years? FV = PV(1 + r/n) ^ntPv = ________ (Be sure to give 2 decimal places of accuracy.)
Answer: PV = 3218.69
Explanation:
The formula for calculating compound interest is expressed as
FV = PV(1 + r/n) ^nt
Where
FV is the future value
PV is the initial value
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
FV = 6500
r = 5.9% = 5.9/100 = 0.059
n = 4 because it was compounded quarterly
t = 12
By substituting these values into the formula,
6500 = PV(1 + 0.059/4)^4 * 12
6500 = PV(1.01475)^48
PV = 6500/(1.01475)^48
PV = 3218.69
If a movie is played at the rate preferred by its director, a moviegoer see 600 frames in 12.5 seconds. how many frames does a moviegoer see in 159?
A moviegoer sees 7632 frames in 159s.
6 cm 4 cm 10 cm What is the area of the figure in square centimeters? TOTAL AREA= find the area of all the shapes and ADD together. To find the area 1/2 of a circle , you need the area of a circle and divide by 2. USE YOUR FORMULA CHART.
Notice that since the bottom side of the figure has a length of 10cm while the part that corresponds to the rectangle is only 6cm long, then the base of the triangle is 4cm long. The height of the triangle is 4cm long, since it is the same as the height of the rectangle. Additionally, the diameter of the semicircle turns out to be equal to 4cm, then its radius (which is half the diameter) must be 2cm long.
Use these data to find the area of each figure:
Semicircle
The area of a semicircle is half the area of a circle:
[tex]\begin{gathered} A=\frac{1}{2}\pi r^2 \\ =\frac{1}{2}\pi(2cm)^2 \\ =2\pi cm^2 \\ \approx6.28cm^2 \end{gathered}[/tex]Rectangle
[tex]\begin{gathered} A=w\times l \\ =6\operatorname{cm}\times4\operatorname{cm} \\ =24cm^2 \end{gathered}[/tex]Triangle
[tex]\begin{gathered} A=\frac{1}{2}b\times h \\ =\frac{1}{2}4\operatorname{cm}\times4\operatorname{cm} \\ =8cm^2 \end{gathered}[/tex]Total area:
[tex]\begin{gathered} A=6.28cm^2+24cm^2+8cm^2 \\ \Rightarrow A=38.28cm^2 \end{gathered}[/tex]Therefore, the total area of the figure is:
[tex]38.28cm^2[/tex]If you randomly select a card from a well-shuffled standard deck of 52 cards, determine the probabilitythat the card you select is not a 6.a) Write your answer as a reduced fraction.b) Write your answer as a decimal, rounded to the nearest thousandth.c) Write your answer as a percent. Round to the nearest tenth of a percent as needed.
Answer:
The probability that a card selected at random is not a 6 is:
a. 12/13
b. 0.923
c. 92.3
Explanation:
There are 4 6's in a well-shuffled deck of cards.
The probability that a card selected at random is not a 6 is:
1 - (The probability that it is a 6)
= 1 - 4/52
= 12/13
b. As a decimal, we have 0.923
c. As a percentage, we have 92.3%
A student earned grades of C, A, B, and A in four different courses. Those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.2.183.408.753.50
Given:
Grades the student earned = C, A, B, A
Corresponding credit hours = 4, 5, 1, 5
The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0.
Required: Grade point average (GPA)
Explanation:
Points earned = Earned grades x Corresponding credit hours
For C, points earned = 2 x 4 = 8 points
For A, points earned = 4 x 5 = 20 points
For B, points earned = 3 x 1 = 3 points
Total points earned = 8+20+3+20 = 51 points
Total credit hours = 4+5+1+5 = 15 hours
Find GPA.
[tex]\begin{gathered} \text{Grade point average\lparen GPA\rparen=}\frac{\text{ Total points of the student}}{\text{ Total credit hours}} \\ =\frac{51}{15} \\ =3.40 \end{gathered}[/tex]Final Answer: The grade point average of the student is 3.40.
in triangle JKL j=10cm k=12cm anf l=13cm find cos K
For the given triangle, we must apply the following trigonometric relation:
[tex]\begin{gathered} k^2=j^2+l^2-2jl\cos K \\ \cos K=\frac{k^2-j^2-l^2}{-2jl} \\ \cos K=\frac{12^2-13^2-10^2}{-2\cdot13\cdot10} \\ \cos K=0.48 \end{gathered}[/tex]Write the coordinates of the vertices after a reflection over the x-axis. 1072
The reflection about x-axis results in same x coodinate with oppositive of y coordinate. It can be expressed as,
[tex](x,y)\rightarrow(x,-y)[/tex]Determine the coordinates of the vertices after reflection over the x-axis.
[tex]Q(6,-8)\rightarrow Q^{\prime}(6,8)[/tex][tex]R(7,-8)\rightarrow R^{\prime}(7,8)[/tex][tex]S(7,-5)\rightarrow Q^{\prime}(7,5)[/tex][tex]T(6,-5)\rightarrow T^{\prime}(6,5)[/tex]pls help me with this one & the ones after it !!!
In the given triangle,
line IF is parallel to line HG,
By the basic proportionality theorem,
[tex]\begin{gathered} \frac{JI}{IH}=\frac{FJ}{FG} \\ \frac{25}{20}=\frac{FJ}{28} \\ \frac{25\cdot28}{20}=FJ \\ FJ=35 \end{gathered}[/tex]Answer: FJ=35
how can we determine key words to find what kind of sign to use
The problem says there are:
2 neighbors with birds
10 neighbors with cats
8 neighbors with dogs.
As each neighbor owns only one pet, the total number of neighbors is then:
2+10+8=20
The percentage of the neighbors that own dogs is the number of neighbors with dogs, divided by the total number of neighbors, then:
[tex]\frac{8}{20}\times100=\frac{4}{10}\times100\text{ \%=0.4x100\%=40\%}[/tex]Then the 40% of the neighborhood pet owners have dogs.
Decide if each fraction expressed as a decimal terminates or repeats.
A. 12/11
B. 5/8
C. -19/20
D. 2/3/6/5
Answer:
A. repeat
B. terminates
C. terminates
D. terminates
Step by step explanation:
to turn the fractions into decimals you have to divide the top by bottom
12÷11=1.0909090909
5÷8=0.625
-19÷20=-0.95
2÷3=0.6666666667 6÷5=1.2 ÷0.6666666667 =0.5555555556
only 1 repeats itself multiple times which means thats the only one the repeats and the rest terminate because they end
In the figure to the right, what value of x makes G the incenter of triangle JKL. See image below
We were given the following information:
LT = 12
GL = 13
GR = x - 3
The incenter of a triangle refers to the intersection point of all interior angle bisectors of the triangle. The incenter is equidistant to the sides, they are all the same
If triangle JKL has G as its incenter, the following will be found to be true:
[tex]|GR|\cong|GS|\cong|GT|[/tex]However, we were not given any of the above distances GR, GS & GT. We can obtain GT by using the Pythagoras Theorem on the triangle GTL as shown below:
[tex]\begin{gathered} |GT|^2=|GL|^2-|LT|^2 \\ |GT|^2=13^2-12^2 \\ |GT|^2=169-144 \\ |GT|^2=25 \\ \text{Take the square root of both sides, we have:} \\ |GT|=\sqrt[]{25} \\ |GT|=5 \\ \\ \therefore|GT|=5 \end{gathered}[/tex]Since GT equals 5, it implies that GS & GT will also equal 5
We will obtain the value of ''x'' as shown below:
[tex]undefined[/tex]Round 58,300 to the nearest ten thousand 
ok
Rounding to the nearest 10000 the result is
60,000
Answer:
60,000
Step-by-step explanation:
The 5 is in the ten-thousands place.
Make all digits right of the 5 into a zero.
You get 50,000.
Since 8 (in the thousands place) is greater than 5, the ten-thousands place goes uo 1 to 6.
Answer: 60,000
Ryan is 6 feet tall. At a certain time of day, he casts a shadow that is 12 feet long. At the same time, a tree casts ashadow that is 28 feet long. What is the height of the tree?
First, notice that Ryan and its shadow form a right triangle with the following measures:
and with the tree, we have the following triangle:
since both triangles are similar, we can write the following proportions:
[tex]\frac{x}{6}=\frac{28}{12}[/tex]where 'x' represent the height of the tree. Solving for 'x', we get:
[tex]\begin{gathered} \frac{x}{6}=\frac{28}{12} \\ \Rightarrow x=\frac{28}{12}\cdot6=\frac{28\cdot6}{12}=\frac{168}{12}=14 \\ x=14ft \end{gathered}[/tex]therefore, the height of the tree is 14 feet
Solve the inequality c+49 <-16
ANSWER
c < -65
EXPLANATION
We have the inequality:
c + 49 < -16
To solve this, we collect like terms:
c < -16 - 49
Simplify:
c < -65
That is the answer.
I need help NUMBER 181.Find the GCF2.Write the GCF 3.Rewrite expression factor out the GCF4. Write the final factored expression!
Answer:
1. Find the GCF:
16 y | 5
1
2. Write the GCF: 1
3. Rewrite expression factor out the GCF: 16y + 5
4. Write the final factored expression: 16y + 5
Explanation:
The initial expression is:
16y + 5
So, we have two terms: 16y and 5
The factors of these terms are:
16y: 1, 2, 4, 16, y, 2y, 4y, 16y
5: 1, 5
So, the greatest common factor is 1
Then, the expression factor out the GCF is:
[tex]\frac{16y+5}{1}=16y+5[/tex]Therefore, the final factored expression is:
1*(16y + 5) = 16y + 5
how do you solve 15w-4=41
In order to solve this equation for w, we can do the following steps:
[tex]\begin{gathered} 15w-4=41 \\ 1.\text{ Add +4 to both sides of the equation:} \\ 15w-4+4=41+4 \\ 15w=45 \\ 2.\text{ Divide both sides of the equation by 15:} \\ \frac{15w}{15}=\frac{45}{15} \\ w=3 \end{gathered}[/tex]So we have that the value of w is 3.
The weight, in pounds, of a male child can be estimated 3 using the function f(x) = 2.69x^3/4, where x represents the child's age in months. Determine the child's weight at 3 years of age, rounded to the nearest thousandth.
the modeled equation for the weight of a male child is
[tex]f(x)=2.69X^{\frac{3}{4}}[/tex]x is the age of the child in months
to calculate the child weight in 3 years
we need to convert the years to months since x is a function of months
12 months ==== 1 year
x months = 3 years
cross multiplication
12 x 3 = 1 * x
x = 36 months
Therefore, 3 years =
disjointed and overlapping events
Answer:
1. P = 0.269 or 26.9%
2. P = 0.372 or 37.2%
Step-by-step explanation:
First, let's calculate the total number of students:
So, we know that the number of students is 662.
Now, let's evaluate the probabilities:
1. Student will begin college during summer AND attend an in-state college.
P = 178/662
P = 0.269 or 26.9%
2. Student will begin college in summer GIVEN THAT he is attending an in-state college.
In this case, the total number of students will be the number of students who will attend an in-state college.
P = 178/479
P = 0.372 or 37.2%
Please help answer questions one through fiveApply the transformation (a to c) on ABC to get an image
Answer:
d) area of the pre- image will be less than the new image
e) it is
Explanation:
Given:
Triangle ABC on a coordinate plane
To find:
the transformation on the original image
We need to state the vertices of the triangle ABC:
A = (-1, 2)
B = (-2, 1)
C = (0, 0)
a) dilation by a scale factor of 4
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen4x, 4y\rparen} \\ A=\text{ \lparen4\lparen-1\rparen, 4\lparen2\rparen\rparen = \lparen-4, 8\rparen} \\ B\text{ = \lparen4\lparen-2\rparen, 4\lparen1\rparen\rparen = \lparen-8, 4\rparen} \\ C=\text{ \lparen4\lparen0\rparen, 4\lparen0\rparen\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]b) reflect over the x axis:
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen x, -y\rparen} \\ We\text{ will negate all the y values of the vertices above while keeping x coordinate constant} \\ A\text{ = \lparen-4, -8\rparen} \\ B\text{ = \lparen-8, -4\rparen} \\ C=\text{ \lparen0, -0\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]c) dilate by 1/2
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow(\frac{1}{2}x,\text{ }\frac{1}{2}y) \\ We\text{ will multiply the coordinates above by 1/2 in both the x and y coordinates} \\ A^{\prime}\text{ = \lparen}\frac{1}{2}(-4),\text{ }\frac{1}{2}(-8))\text{ = \lparen-2, -4\rparen} \\ B^{\prime}\text{ = \lparen}\frac{1}{2}(-8),\text{ }\frac{1}{2}(-4))\text{ = \lparen-4, -2\rparen} \\ C^{\prime}\text{ = \lparen}\frac{1}{2}(0),\text{ }\frac{1}{2}(0))\text{ = \lparen0, 0\rparen} \\ \\ Image\text{ of ABC: A' \lparen-2, -4\rparen, B' \lparen-4, -2\rparen and C' = \lparen0, 0\rparen} \end{gathered}[/tex]d) To determine if the area of the pre-image is greater or less than, we will plot the coordinates of both triangles:
Since the triangle of the Image is greater than the triangle of the pre-image (original figure), then the area of the pre- image will be less than the new image
e) For two triangles to be congruent, the sides and angles for both triangles will be equal
For two triangles to be similar, the ratio of their corresponding sides will be equal
The image A'B'C' is a scaled triangle of ABC. This mean the sides can't be equal but the ratio fo their corresponding sides will be equal.
Hence, it is simlar
I’m getting 57.14 inches for perimeter and 114.29 for area, am I correct? Have struggled a little
Part 1
Find out the perimeter
The perimeter of the figure is given by
[tex]\begin{gathered} P=\pi(8)+8+8 \\ P=16+8\pi \\ P=41.13\text{ in} \end{gathered}[/tex]The perimeter is 41.13 inchespart 2
Find out the area
The area is given by
[tex]\begin{gathered} A=\pi(4^2)+8^2 \\ A=16\pi+64 \\ A=114.27\text{ in2} \end{gathered}[/tex]The area is 114.27 square inchesWhat is the value of the algebraic expression if x = 1/2, y = -1, and z = 2?Here is the algebraic expression: 6x(y to second power z)
The value of the algebraic expression if x = 1/2, y = -1, and z = 2 is 6.
The given expression is [tex]6xy^{2}z[/tex] and we need to evaluate its value when x = 1/2, y = -1, and z = 2
Simply assign the values of each variable to the variables in the algebraic expression and evaluate the result to get the value of the expression. What we do is:
[tex]6xy^{2}z\\\\=6 * \frac{1}{2}*(-1)^{2} *2 \\\\=6 * \frac{1}{2}*1 *2\\\\=6[/tex]
The algebraic expression's value would be 6, then. In an algebraic expression, the variables are denoted by letters, in this case x, y, and z; the coefficients are denoted by numbers, such as 6, and the exponents are, in this case, 2, as in the expression above. Expressions frequently include several terms made up of those components.
To read more about algebraic expressions, visit https://brainly.com/question/953809
#SPJ9
Find the lateral surface area of the rectangular prism. Round your answer to the tenth of necessary
48 square feet
Explanation
to find the lateral surafece, we need to add the 4 faces that make it,so
so,the total area
[tex]\begin{gathered} \text{Area}=2(\text{length}\cdot\text{width)}+2(\text{length}\cdot\text{width)} \\ \text{Area}=2(6\text{ ft}\cdot3\text{ ft)+2(3ft}\cdot\text{2 ft)} \\ \text{Area}=2(18ft^2)+2(6ft^2) \\ \text{Area}=36ft^2+12ft^2 \\ \text{Area}=48ft^2 \end{gathered}[/tex]so, the answer is 48 square feet