Suppose that $88 comma 00088,000 is invested at 3 and one half3 1 2% interest, compounded quarterly. a) find the function for the amount to which the investment grows after t years
A rectangle has a base of 3 inches and a height of 9 inches. If the dimensions are doubled, what will happen to the area of the rectangle?
Answer:
Area will increase by 4 times
Step-by-step explanation:
Given: A rectangle has a base of 3 inches and a height of 9 inches.
To find: If the dimensions are doubled, what will happen to the area of the rectangle?
Solution:
It is given that a rectangle has a base of 3 inches and a height of 9 inches.
Now, to find if the dimensions are doubled what will happen to the area, first we need to find the original area.
Original area of rectangle, when base is 3 inches and height 9 inches is
[tex]9\times3=27[/tex] square inches
Now, when dimensions are doubled , the base becomes 6 inches and height becomes 18 inches
So, new area becomes [tex]6\times18=108[/tex] square inches.
Now,
[tex]\frac{\text{new area}}{\text{original area} }=\frac{108}{27}[/tex]
[tex]\implies\frac{\text{new area}}{\text{original area} }=\frac{4}{1}[/tex]
Hence, the area will increase by 4 times.
16x^2=100
How many solutions will there be to the following equation?
Answer:
There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex]16x^2=100[/tex]
To find : How many solutions will there be to the following equation?
Solution :
Equation [tex]16x^2=100[/tex]
Solve the equation,
Divide by 16 both side,
[tex]\frac{16x^2}{16}=\frac{100}{16}[/tex]
[tex]x^2=\frac{100}{16}[/tex]
Taking root both side,
[tex]x=\sqrt{\frac{100}{16}}[/tex]
[tex]x=\sqrt{\frac{10^2}{4^2}}[/tex]
[tex]x=\pm\frac{10}{4}}[/tex]
[tex]x=\pm\frac{5}{2}}[/tex]
Therefore, There are two solutions [tex]x=\frac{5}{2},-\frac{5}{2}[/tex]
Circle A is inscribed in a quadrilateral. What is the perimeter of the quadrilateral?
A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. what is the probability that at least one of the calculators is defective?
Find the y-intercept and x-intercept of the line.
5x - 4y = 15
y-intercept: __
x-intercept: __
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.
Answer:
x^2/25 + y^2/81 =1
Step-by-step explanation:
solved it
Given a polynomial f(x), if (x + 7) is a factor, what else must be true? Help plzzz im running out of time
f(0) = 7
f(0) = −7
f(−7) = 0
f(7) = 0
In triangle ABC, angle B = 30°, a = 210, and b = 164. The measure of angle A to the nearest degree is a0
The length of the third side of the triangle would be 106.5 units approx.
What is a triangle?A triangle is a two - dimensional figure with three sides and three angles.
The sum of the angles of the triangle is equal to 180 degrees.
∠A + ∠B + ∠C = 180°
Given is that in triangle ABC, angle B = 30°, a = 210, and b = 164.
The cosine formula is given as follows -
c² = a² + b² + 2abcos(α)
c = √(a² + b² + 2abcos(α))
c = √(210)² + (164)² + 2(210)(164)cos(30°)
c = 106.5 units approx.
Therefore, the length of the third side of the triangle would be 106.5 units approx.
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The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The area of the base is __________ The volume is ________
Answer:- The area of base is 52900 square meters. The volume is 2654000 cubic meters.
Explanation:-
Base length of right pyramid (square) a =230m
Height of right pyramid = 150m
Area of base of right pyramid[tex]=a^2=(230)^2=52900\ m^2[/tex]
Volume of right pyramid with square base[tex]=\frac{1}{3}a^2h\\=\frac{1}{3}\times52900\times150=2645000\ m^3[/tex]
Thus, the area of base is 52900 square meters and the volume is 2654000 cubic meters.
The area of the base of the pyramid is 52900 m²
The volume of the square base pyramid of Giza is 2645000 m³
The pyramid is a square base pyramid. Therefore,
volume of a square base pyramid;v = 1 / 3 Bhwhere
B = base area
h = height
h = 150 m
Therefore,
area of the base = l²
where
l = length of side
area of the base = 230² = 52900 m²
Volume = 1 / 3 × 52900 × 150
volume = 7935000 / 3
volume = 2645000 m³
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Find the missing values for the exponential function represented by the table below.
xy
-2 4
-1 6
0 9
1
2
a.
-13.5
-20.25
c.
6
4
b.
-13.5
20.25
d.
13.5
20.25
Answer: c.
6
4
Step-by-step explanation:
The exponential function is given by :-
[tex]y=Ab^x[/tex], where A is the initial amount , b is common ratio and x is time period.
We know that in exponential functions, the ratio of the consecutive value of y is same.
From the table , [tex]b=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
At x = 0
[tex]9=A(\dfrac{2}{3})^0\\\\\Rightarrow\ A=9[/tex]
At x=1
[tex]y=9(\dfrac{2}{3})^1=6[/tex]
At x=2
[tex]y=9(\dfrac{2}{3})^2=4[/tex]
Hence, the missing values for the exponential function : c. 6 4.
For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?
The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.
The test result is not significant at α = 0.05 or α = 0.01.
For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Given the information provided, the result is not significant at either α = 0.05 or α = 0.01. This conclusion is drawn based on the p-value and the 95% confidence interval.
On compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. The correct options B.
To determine the significance of the test statistic at different levels of significance, we need to compare it to critical values associated with the chosen alpha levels.
Given that the test statistic is 2.2, we need to refer to the critical values of the test statistic for a two-tailed test at α = 0.05 and α = 0.01. These critical values are typically obtained from statistical tables or software.
Let's assume the critical value at α = 0.05 is [tex]\( z_{\alpha/2} = \pm 1.96 \)[/tex]and the critical value at α = 0.01 is [tex]\( z_{\alpha/2} = \pm 2.58 \)[/tex](for a standard normal distribution).
If the test statistic falls within the range defined by these critical values, we can conclude that the result is significant at the corresponding alpha level. Otherwise, the result is not significant.
Since the test statistic of 2.2 falls between the critical values of [tex]\( \pm 1.96 \)[/tex] for α = 0.05 but outside the critical values of [tex]\( \pm 2.58 \)[/tex] for α = 0.01, we can conclude that:
The result is significant at α = 0.05 but not at α = 0.01.
Final answer: The result is significant at α = 0.05 but not at α = 0.01.
We compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. This interpretation aligns with standard hypothesis testing procedures.
Complete question
For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?
A)The result is significant at both α = 0.05 and α = 0.01.
B)The result is significant at α = 0.05 but not at α = 0.01.
C)The result is significant at α = 0.01 but not at α = 0.05.
D)The result is not significant at either α = 0.05 or α = 0.01.
E)The result is inconclusive because we don't know the value of p.
For what values of x does f(x) = x^2 +5x +6 reach its minimum value?
The minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.
To find the minimum value of the quadratic function [tex]\( f(x) = x^2 + 5x + 6[/tex], we can use the vertex formula. The vertex of a quadratic function [tex]\( ax^2 + bx + c \) is given by the point \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]
[tex]For \( f(x) = x^2 + 5x + 6 \), \( a = 1 \), \( b = 5 \), and \( c = 6 \).[/tex]
The x-coordinate of the vertex is [tex]\( -\frac{b}{2a} = -\frac{5}{2(1)} = -\frac{5}{2} \).[/tex]
To find the minimum value, we substitute [tex]\( x = -\frac{5}{2} \)[/tex] into the function:
[tex]\[ f\left(-\frac{5}{2}\right) = \left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 6 \]\[ = \frac{25}{4} - \frac{25}{2} + 6 \]\[ = \frac{25}{4} - \frac{50}{4} + \frac{24}{4} \]\[ = \frac{-1}{4} \][/tex]
So, the minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.
which statement is true about angles 1 and 2
Answer:
Option a) They are adjacent angles
Step-by-step explanation:
Given is a picture of a graph with angles 1 to 6 around it.
Out of these angle 2 and 5 are right angles.
1 and 2 are adjacent to each other.
They are not complementary because 1+2 not equals 90
They are neither supplementary since sum does not equal 180
They cannot be vertical because they are not formed by intersection of two lines.
Hence only option a is right
Option a) They are adjacent angles
Kara has 90 lollipops, 36 chocolate bars, and 72 gumballs to put in goody bags for her party. What is the largest number of goody bags that Kara can make so that each goody bag has the same number of lollipops, the same number of chocolate bars, and the same number of gumballs?
The largest number of goody bags that Kara can make are [tex]18[/tex] .
What is Highest Common Factor ?Highest or greatest Common Factor is the largest common factor that all the numbers have in common.
We have,
Number of Lollipops [tex]=90[/tex]
Number of chocolate bars [tex]=36[/tex]
Number of gumballs [tex]=72[/tex]
So,
To find the number of bags;
First find out the Highest Common Factor of [tex]90,36,72[/tex];
[tex]90=2*3*3*5[/tex]
[tex]36=2*2*3*3[/tex]
[tex]72=2*2*2*3*3[/tex]
So, from the factors of all numbers we have,
Highest Common Factor [tex]=18[/tex]
Now,
Lollipops [tex]=\frac{90}{18} =5[/tex]
Chocolate bars [tex]=\frac{36}{18} =2[/tex]
Gumballs [tex]=\frac{72}{18} =4[/tex]
So, the largest number of goody bags that Kara can make are [tex]18[/tex] so that each goody bag has [tex]5[/tex] number of lollipops, [tex]2[/tex] number of chocolate bars, and [tex]4[/tex] number of gumballs.
Hence, we can say that the largest number of goody bags that Kara can make are [tex]18[/tex] .
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Find the value of 'y' in the equation 3/y-3 =8
A.) y= -2 3/8
B.) y= -1 5/8
C.) y= 1 5/8
D.) y= 2 3/8
The following is a geometric sequence 5,3,1,-1
I need some assistance in figuring this out
PLEASE HELP IMAGE ATTACHED! These triangles are similar. Find the area of the smaller triangle to the nearest whole number.
The area of smaller triangle is 59 square feet
What are the similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
What is the formula for the area of triangle?The formula for the area of triangle is
[tex]Area = \frac{1}{2} \times base \times \ height[/tex]
According to the given question.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore,
[tex]\frac{y}{x} = \frac{16}{12}[/tex]
[tex]\implies y = \frac{4}{3} x[/tex]
Also, the area of larger triangle is 105 square feet.
[tex]\implies \frac{1}{2} \times \frac{4}{3} x \times 16 = 105[/tex]
The above euqtaion can be written as
[tex]\implies \frac{1}{2}\times \frac{4}{3} x \times \frac{4}{3} \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times (\frac{4}{3} )^{2} \times x \times 12 = 105[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 105 \times \frac{9}{16}[/tex]
[tex]\implies \frac{1}{2} \times x \times 12 = 59[/tex]
⇒ Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
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The scale of a map is 0.5 inch : 20 miles. on the map, the distance between two cities is 1.5 inches. what is that actual distance between the two cities?
Answer:
60 miles.
Step-by-step explanation:
We have been given that the scale map is 0.5 inch : 20 miles. On the map, the distance between two cities is 1.5 inches. We are asked to find the actual distance between the two cities.
We will use proportions to solve for the actual distance between both cities as:
[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]
[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}*\text{1.5 inches}=\frac{20\text{ miles}}{\text{0.5 inch}}*\text{1.5 inches}[/tex]
[tex]\text{Actual distance}=20\text{ miles}*3[/tex]
[tex]\text{Actual distance}=60\text{ miles}[/tex]
Therefore, the actual distance between both cities is 60 miles.
Hey rectangular pan has a link that is for third the with the total area of the pan is 432 in.² what is the width of the cake pan
On monday eliza read her book. on tuesday she read three times as long as she read on monday. on wednesday she read 20 minutes less than tuesday. on thursday she read for 20 minutes which was half as long as she read on wednesday. how many minutes did eliza read over the 4-day period
Solve for the unknown side.
last option is none of these
The side of the triangle which is the hypotenuse side is [tex]2\sqrt{13}[/tex]
What is the hypotenuse side?Using trigonometry, Trigonometry is the area of mathematics that deals with particular angle functions and how to use them in computations. In trigonometry, an angle can have six common functions. The terms sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their names and abbreviations.
[tex]c^{2} =4^{2} +6^{2} \\\\c^{2}=16+36\\\\c^{2}=52\\\\c=\sqrt{52} \\\\c= 2\sqrt{13}[/tex]
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If x is inversely proportional to y, and x = 60 when y = 0.5, find x when y = 12. A. 0.4 B. 25 C. 360 D. 2.5
Which of the following equations have graphs that are parallel to the graph of the equation y=-3/2x+8?
I. 3x + 2y = 10
II. 2x − 3y = 9
III. 6x + 4y = 28
IV. 3x − 2y = 8
I and III only
II and III only
IV only
III only
Which equation is equivalent to 4s=t+2
a. s=t-2
b. s=4/t+2
c. s=t+2/4
d. s=t+6
the equivalent equation of the equation 4s=t+2 is s = [tex]\frac{t+2}{4}[/tex] .
What is Equivalent equations?Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
According to the question
The equation
4s=t+2
Now,
its Equivalent equations is :
Dividing equation by 4 both side
i.e
s = [tex]\frac{t+2}{4}[/tex]
Hence , the equivalent equation of the equation is s = [tex]\frac{t+2}{4}[/tex] .
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Given: The coordinates of iscosceles trapezoid JKLM are J(-b, c), K(b,c), L(a,0), and M(-a,0).
Prove: The diagonals of an isosceles trapezoid are congruent.
As part of the proof, find the length of KM
A) a2+b2+c2
B) (-a+b)2+c2
C) (a+b)2+c2
Answer with explanation:
It is given that, coordinates of Isosceles trapezoid J K L M are J(-b, c), K(b,c), L(a,0), and M(-a,0).
To Prove: The diagonals of an isosceles trapezoid are congruent.
Proof:
Distance formula , that is distance between two points in x y plane is given by
[tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Where, [tex](x_{1},y_{1}),(x_{2},y_{2})}[/tex] are coordinates of two points in the plane.
Length of Diagonal J L
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
Length of Diagonal K M
[tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]
So, we can see that,
J L = KM [tex]=\sqrt{(a+b)^2+(c)^2}[/tex]
Hence,The diagonals of an isosceles trapezoid are congruent.
So ,
[tex]KM=\sqrt{(a+b)^2+c^2}[/tex]
Option C
A turtle is 20 5/6 inches below the surface of a pond. It dives to a depth of 32 1/4 inches. What was the change in the turtles position? Write your answer as a mixed number and show your work.
Math help needed. Thank you
Determine how many, what type, and find the roots for f(x) = x^3 - 5x^2 – 25x + 125