Answer:
Sin(E) = 7/25
Sin(D) = 24/25
Tan(D)= 24/7
Step-by-step explanation:
Sin=opp/hyp
Tan=opp/adj
Cos=adj/hyp
The trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
How to determine the trigonometric ratios?The given parameters are:
EF = 24
DF = 7
Start by calculating the length DE using:
DE²= EF² + DF²
So, we have:
DE²= 24² + 7²
Take the square root of both sides
DE= 25
The sine of the angles is calculated using:
sin(Ф) = opp/hyp
So, we have:
sin(E) = 7/25
sin(D) = 24/25
The tangent of the angles is calculated using:
tan(Ф) = opp/adj
So, we have:
tan(D)= 24/7
Hence, the trigonometric ratios that are correct for triangle DEF are sin(E) = 7/25, sin(D) = 24/25 and tan(D)= 24/7
Read more about trigonometric ratios at:
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City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a population that is growing exponentially. In the year 2000, there were half as many people in B as in A. In the year 2010, the population of A was 20% more than the population of B.
When will the populations be equal? Give your answer in years after 1990.
Answer:
City A and city B will have equal population 25years after 1990
Step-by-step explanation:
Given
Let
[tex]t \to[/tex] years after 1990
[tex]A_t \to[/tex] population function of city A
[tex]B_t \to[/tex] population function of city B
City A
[tex]A_0 = 10000[/tex] ---- initial population (1990)
[tex]r_A =3\%[/tex] --- rate
City B
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010
Required
When they will have the same population
Both functions follow exponential function.
So, we have:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
Calculate the population of city A in 2000 (t = 10)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]
[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]
[tex]A_{10} = 10000 * (1.03)^{10}[/tex]
[tex]A_{10} = 13439.16[/tex]
Calculate the population of city A in 2010 (t = 20)
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]
[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]
[tex]A_{20} = 10000 * (1.03)^{20}[/tex]
[tex]A_{20} = 18061.11[/tex]
From the question, we have:
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] and [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]
[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]
[tex]B_{10} = 6719.58[/tex]
[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]
[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]
[tex]18061.11 = B_{20} * (1.20)[/tex]
Solve for B20
[tex]B_{20} = \frac{18061.11}{1.20}[/tex]
[tex]B_{20} = 15050.93[/tex]
[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
For: [tex]B_{10} = 6719.58[/tex]
We have:
[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
For: [tex]B_{20} = 15050.93[/tex]
We have:
[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]
[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]
Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]
[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]
Apply law of indices
[tex](1 + r_B)^{20-10} = 2.2399[/tex]
[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)
Take 10th root of both sides
[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]
[tex]1 + r_B = 1.08[/tex]
Subtract 1 from both sides
[tex]r_B = 0.08[/tex]
To calculate [tex]B_0[/tex], we have:
[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]
Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]
So:
[tex]B_0 * 2.2399 = 6719.58[/tex]
[tex]B_0 = \frac{6719.58}{2.2399}[/tex]
[tex]B_0 = 3000[/tex]
Hence:
[tex]B_t = B_0 * (1 + r_B)^t[/tex]
[tex]B_t = 3000 * (1 + 0.08)^t[/tex]
[tex]B_t = 3000 * (1.08)^t[/tex]
The question requires that we solve for t when:
[tex]A_t = B_t[/tex]
Where:
[tex]A_t = A_0 * (1 + r_A)^t[/tex]
[tex]A_t = 10000 * (1 + 3\%)^t[/tex]
[tex]A_t = 10000 * (1 + 0.03)^t[/tex]
[tex]A_t = 10000 * (1.03)^t[/tex]
and
[tex]B_t = 3000 * (1.08)^t[/tex]
[tex]A_t = B_t[/tex] becomes
[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]
Divide both sides by 10000
[tex](1.03)^t = 0.3 * (1.08)^t[/tex]
Divide both sides by [tex](1.08)^t[/tex]
[tex](\frac{1.03}{1.08})^t = 0.3[/tex]
[tex](0.9537)^t = 0.3[/tex]
Take natural logarithm of both sides
[tex]\ln(0.9537)^t = \ln(0.3)[/tex]
Rewrite as:
[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]
Solve for t
[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]
[tex]t = 25.397[/tex]
Approximate
[tex]t = 25[/tex]
Help!!!!!!!!!!! Photo attached
Answer:
option A : 25
Step-by-step explanation:
Given :
P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)
Find the length of PQ ,QR , PR.
Using distance formula to find the lengths.
[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]
[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]
Clearly , the triangle satisfies Pythagoras theorem :
Square of larger side = Sum of squares of other sides.
Therefore , PQR is a right triangle,
with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .
[tex]Area = \frac{1}{2} \times base \times height[/tex]
[tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]
f(x)=[tex]\frac{3}{x+2}[/tex]-[tex]\sqrt{x-3}[/tex]
f(x) = 3/x+2 - √x - 3
We can put any value of x so, let x be 3f(3) = 3/3 + 2 - √3 - 3
f(3) = 3/3 + 2 - √0
f(3) = 3/5 - 0
f(3) = 3/5
You can let x be any value of your choice.
Find f(-2) for f(x) = 3x2^x
The value of function f (- 2) would be,
⇒ f (- 2) = 3 / 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The value of function is,
⇒ f (x) = 3 × 2ˣ
Now,
At x = - 2;
The value of function f (- 2) would be,
⇒ f (x) = 3 × 2ˣ
⇒ f (- 2) = 3 × 2⁻²
⇒ f (- 2) = 3 × 1 / 4
⇒ f (- 2) = 3 / 4
Thus, The value of function f (- 2) would be,
⇒ f (- 2) = 3 / 4
Learn more about the function visit:
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4th grade math question:
jessica bought 4 gallons of paint. Jessica needed to use 3/4 of the paint to paint her living room and dining room. How many gallons did she use, write the number of gallons.
Answer:
1 gallon
Step-by-step explanation:
gallons of paint needed; 4
gallons used: (3/4)*4
= 1 gallon was used
Answer:
Answer is 3 gallons
Step-by-step explanation:
1 gallon= 25%
2 gallons=50%
3 gallons=75%
3/4 is equivalent to 75%
Hope this helped!
The following hypothetical data represent a sample of the annual numbers of home fires started by candles for the past several years.
5640, 5090, 6590, 6380, 7165, 8440, 9980
The population has a standard deviation equal to 1210. Assuming that the data is from a distribution that is approximately normal, construct a 90 % confidence interval for the mean number of home fires started by candles each year
Answer:
(6290.678 ; 7790.742)
Step-by-step explanation:
Given the data :
5640, 5090, 6590, 6380, 7165, 8440, 9980
The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71
The 90% confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 90% confidence = 1.64
Hence,
Margin of Error = 1.64 * 1210/√7
Margin of Error = 750.032
90% confidence interval is :
7040.71 ± 750.032
Lower boundary = 7040.71 - 750.032 = 6290.678
Upper boundary = 7040.71 + 750.032 = 7790.742
(6290.678 ; 7790.742)
Evaluate the function.
f(x) = 2x2
Find f(-3)
Can anybody answer this?
Answer:
18
Step-by-step explanation:
f(x) = 2x^2
Let x = -3
f(-3) = 2 * (-3)^2
Exponents first
f(-3)=2 *9
f(3) = 18
Answer:
f ( - 3 ) = 18
Step-by-step explanation:
f ( x ) = 2x²
Find f ( - 3)
let , x = - 3
lf ( - 3 ) = 2 ( -3 )²
f ( - 3 ) = 2 × ( - 3 )²
Evaluate the power
f ( -3) = 2 × 9
multiply the numbers
f ( - 3 ) = 18
Solve x2 – 8x + 15 < 0.
Select the critical points for the inequality shown.
Answer:
x> 17/8
Step-by-step explanation:
add the numbers
17-8x<0
move the constant to the right-hand side and change its sign
-8x<-17
Divide both side of the inequality by -8 and flip the inequality sign
x>17/8
What is the answer to this?
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
Answer:
The answer is "The second choice".
Step-by-step explanation:
[tex]r=6\\\\h=13 \\\\[/tex]
Formula:
[tex]A=2\pi rh[/tex]
[tex]=2\times 3.14 \times 6 \times 13\\\\=2\times 3.14 \times 78\\\\=3.14 \times 156\\\\=3.14 \times 156\\\\=489.84 \approx 489.8 ft^2[/tex]
The net of a solid figure is shown below:
Which calculation will give the total surface area of the solid figure? (1 point)
1) 5.6.6 square inches
2) 6.5.5 square inches
3) 6.5.5.5 square inches
4) 5.6.6.6 square inches
===========================================================
Explanation:
Each square has a side length of 5 inches, so each square has area 5*5 = 25 square inches. We have 6 such squares to give a total surface area of 6*25 = 150 square inches.
Effectively, this is the same as using the formula below
S = 6x^2
S = 6*5^2
S = 6*5*5
S = 150
x = 5 refers to the side length and S is the surface area. It might help to cut the figure from the paper, and fold it up and you should find that a 3D box will form. There are 6 faces with area of 5*5 each, hence the 6*5*5
A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 10 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
The area of the bookmark is cm2.
Plzz help me
Answer:
Area of the bookmark = 52.56 cm²
Step-by-step explanation:
The two semicircles attached at both end of the rectangle will give us a full circle.
Therefore,
Area of the bookmark = area of rectangle + Area of a circle
Area of the bookmark = L × W + πr²
Length (L) = 10 cm
Width (W) = 4 cm
radius (r) = ½(4) = 2 cm
π = 3.14
Plug in the values into the equation
Area of bookmark = 10 × 4 + 3.14 × 2²
= 40 + 12.56
= 52.56 cm²
Which of the following expressions are equivalent to 52n+n4n2 + 4n
5
2
n
+
n
4
n
2
+
4
n
?
Answer:
they just go straight what does it mean?
A teacher wishes to choose a group of students to help with a presentation. If he needs 2 boys and 3
girls to help with the project and has 14 boys and 12 girls in his classroom, in how many ways can he
make the selection?
Which number line represents the solution set for the inequality -4(x + 3) S-2 – 2x?
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7
+
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2:-1 0 1
2.
+
6
+
7
3 4
01
5
02
Answer:
the answer is the alphabet A at the picture
The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A
Inequality expressionGiven the inequality expression
-4(x+3) <= -2-2x
Expand the inequality
-4x - 12 <= -2-2x
Collect the like terms
-4x + 2x <= -2+12
-2x <= 10
Divide both sides by -2
-2x/-2 >= 10/-2
x >= -5
For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.
Learn more on inequality expression: https://brainly.com/question/24372553
Three lines intersect at point P, as shown in the diagram below. Find the measure of
Answer:
VPQ = 83°
Step-by-step explanation:
You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:
SPR = UPV; TPU = RPQ; TPS = VPQ
360 - SPR - UPV - RPQ - TPU = VPQ + TPS
As some of they are equal, we can just multiply they by 2:
360 - 2×SPR - 2×RPQ = 2× VPQ
360 - 2×35 - 2×62 = 2×VPQ
360 - 70 - 124 = 2×VPQ
2 VPQ = 166
VPQ = 166/2
VPQ = 83°
What is the surface area and volume of the sphere shown below?
Your response should show all necessary calculations and diagrams.
Answer:
ur mom
Step-by-step explanation:
doin doin
Let f(x)=x2+10x+37 .
What is the vertex form off(x)?
What is the minimum value off(x)?
Enter your answers in the boxes.
Vertex form: f(x)=
Minimum value of f(x):
Answer:
f(x) = (x+5)^2 +12
The minimum value is 12
Step-by-step explanation:
f(x)=x^2+10x+37
The vertex will be the minimum value since this is an upwards opening parabola
Completing the square by taking the coefficient of x and squaring it adding it and subtracting it
f(x) = x^2+10x + (10/2) ^2 - (10/2) ^2+37
f(x) = ( x^2 +10x +25) -25+37
= ( x+5) ^2+12
Th is in vertex form y = ( x-h)^2 +k where (h,k) is the vertex
The vertex is (-5,12)
The minimum is the y value or 12
100 POINTS HELP ME NOW!
Answer:
[tex]160[/tex]
Step-by-step explanation:
A rectangular prism's surface area is [tex]2(wl+hl+hw)[/tex].
2·(10·5+2·5+2·10)=160.
Answer:
a or c
Step-by-step explanation:
surry if im wrong
How far does a train travel in 12 hours at 115 miles per hour?
1,509 mi
1,265 mi
1,380 mi
Answer:1380
Step-by-step explanation: 12x115
Answer:
1,380
Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)
Hope this is helpful
PLEASE HELP!! Please answer all if you can and show answer clearly thankyou sm if u do
Answer:
Below:
Step-by-step explanation:
A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)
B) 0.45
C) 0.40
A) the total probability has to equal 1.
To find the probability of rat subtract the other animals from1:
Rat = 1 - 0.35-0.4-0.1 = 0.15
Rat = 0.15
B) probability of cat or hamster equals the sum of their probabilities:
Cat = 0.35 + hamster = 0.1 = 0.45
Answer = 0.45
C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16
Answer = 0.16
The functions f(x) and g(x) are defined below. (in the image attached)
Which expression is equal to f(x) + g(x)?
[tex] \frac{2x - 20}{ {x}^{2} + 6x - 40 } [/tex]
This is the right answer.
Refer to the attachment for the complete work.
Charlie (c) has 75 more pencils than Kate (k). Together, they have 135 pencils. How many pencils does Kate have? *
Answer:
60
Step-by-step explanation:
135-75 = 60
HOPE IT HELPS
PLEASSSSSSSSSSSEEEEEEEE HELPPP IM BEGGING SOMEONE PLEASEEEEEEEE PLEASEEEEEEEEEEE HELPPPP
Answer:
20 degree
Step-by-step explanation:
x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)
2x = 110 - 70
x = 40/2
x = 20 degree
2. How many miles the trucks will have to drive for the costs of the trucks to be equal?
Step-by-step explanation:
kayo na po bahala mag calculate
really need help quick GR5 question
Answer:
Amount won : $3,000,000
Step-by-step explanation:
Let the amount won be =100 x
Amount spent on house :
[tex]\frac{4}{5} \ of \ 100 x = 80 x[/tex]
Remaining amount = 100x - 80x = 20x
Amount spent on yacht :
[tex]\frac{3}{4} \ of \ 20x = 15x[/tex]
Remaining amount = 20x - 15x = 5x
Amount spent on a trip :
[tex]\frac{2}{3} \ of \ 5x = \frac{10}{3}x[/tex]
Remaining amount =
[tex]5x - \frac{10}{3}x = \frac{15x -10x}{3} = \frac{5x}{3}[/tex]
This amount is given for charity :
[tex]\frac{5}{3}x[/tex]
But given :
Amount given to charity is 50000
Therefore ,
[tex]\frac{5}{3}x = 50000[/tex]
[tex]5x = 3 \times 50000\\\\5x = 150000\\\\x = 30000[/tex]
Therefore , the amount won on lottery is = 100x = 100 ( 30000) = 3,000,000
The amount of money he won
What is an equation that represents the line that passes through the points (1, 1) and (-2, 7)?
a piece of ribbon is 5.4 meters long. What will be the length of 8 similar pieces?
Answer:
43.2 meters
Step-by-step explanation:
Multiply the length of one piece of ribbon by 8 to determine the total length
5.4 * 8 =43.2 meters
Get brainiest if right!!!
10points if right!!
Answer:
the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)
the formula is 0.3*0.5^n-1
the formula for finding the nth term of a geometric sequence preset would be
a*r^n-1
a is first term
r is common ratio
Step-by-step explanation:
Reeba is baking cookies for the bake sale. She bakes 3 ¾ dozen chocolate chip cookies to sell . If Reeba sells ⅔ of the cookies, how many cookies did she sell?
Answer:
30 cookies
Step-by-step explanation:
Reeba sells [tex]\frac{2}{3}[/tex] of [tex]3\frac{3}{4}[/tex] of 12 chocolate chip cookies.
Let us start by finding [tex]3\frac{3}{4}[/tex] of 12. We simply have to multiply the two numbers. However, it would be much easier if we had an improper fraction than a mixed number. Let us make [tex]3\frac{3}{4}[/tex] an improper fraction first.
[tex]3\frac{3}{4} =\frac{15}{4}[/tex]
Ok! Let's multiply.
[tex]\frac{15}{4} *\frac{12}{1} =\\15*3\\=45[/tex]
Ok, Reeba baked 45 cookies in total. We know that she sells [tex]\frac{2}{3}[/tex] of her baked cookies, so we can again multiply the two numbers.
[tex]\frac{2}{3} *\frac{45}{1} =\\2*15=\\30[/tex]
Therefore, Reeba sold 30 cookies.
I hope this helps! Let me know if you have any questions :)